Solved: An ideal gas expands while the pressure is kept

Two moles of an ideal gas are heated at constant pressure from to (a) Draw a pV-diagram for this process. (b) Calculate the work done by the gas

Six moles of an ideal gas are in a cylinder fitted at one end with a movable piston. The initial temperature of the gas is and the pressure is constant. As part of a machine design project, calculate the final temperature of the gas after it has done 2.40 * 10 of work.

CALC Two moles of an ideal gas are compressed in a cylinder at a constant temperature of 65.0°C until the original pressure has tripled. (a) Sketch a pV-diagram for this process. (b) Calculate the amount of work done.

Work Done by the Lungs. The graph in Fig. E19.4 shows a pVdiagram of the air in a human lung when a person is inhaling and then exhaling a deep breath. Such graphs, obtained in clinical practice, are normally somewhat curved, but we have modeled one as a set of straight lines of the same general shape. (Important: The pressure shown is the gauge pressure, not the absolute pressure.) (a) How many joules of net work does this persons lung do during one complete breath? (b) The process illustrated here is somewhat different from those we have been studying, because the pressure change is due to changes in the amount of gas in the lung, not to temperature changes. (Think of your own breathing. Your lungs do not expand because theyve gotten hot.) If the temperature of the air in the lung remains a reasonable 20C, what is the maximum number of moles in this persons lung during a breath?

During the time 0.305 mol of an ideal gas undergoes an isothermal compression at 468 J of work is done on it by the surroundings. (a) If the final pressure is 1.76 atm, what was the initial pressure? (b) Sketch a pV-diagram for the process.

A gas undergoes two processes. In the first, the volume remains constant at \(0.200\mathrm{\ m}^3\) and the pressure increases from \(2.00 \times 10^5\mathrm{\ Pa}\ to\ 5.00 \times 10^5\mathrm{\ Pa}\). The second process is a compression to a volume of \(0.120\mathrm{\ m}^3\) at a constant pressure of \(5.00\times 10^5\mathrm{\ Pa}\). (a) In a \(p V \text {-diagram, }\) show both processes. (b) Find the total work done by the gas during both processes.

Work Done in a Cyclic Process. (a) In Fig. 19.7a, consider the closed loop \(1 \rightarrow 3 \rightarrow 2 \rightarrow 4 \rightarrow 1\). This is a cyclic process in which the initial and final states are the same. Find the total work done by the system in this cyclic process, and show that it is equal to the area enclosed by the loop. (b) How is the work done for the process in part (a) related to the work done if the loop is traversed in the opposite direction, \(1 \rightarrow 4 \rightarrow 2 \rightarrow 3 \rightarrow 1\)? Explain.

Figure E19.8 shows a pV-diagram for an ideal gas in which its absolute temperature at b is one-fourth of its absolute temperature at a. (a) What volume does this gas occupy at point b? (b) How many joules of work was done by or on the gas in this process? Was it done by or on the gas? (c) Did the internal energy of the gas increase or decrease from a to b? How do you know? (d) Did heat enter or leave the gas from a to b? How do you know?

A gas in a cylinder expands from a volume of to Heat flows into the gas just rapidly enough to keep the pressure constant at during the expansion. The total heat added is (a) Find the work done by the gas. (b) Find the change in internal energy of the gas. (c) Does it matter whether the gas is ideal? Why or why not?

Five moles of an ideal monatomic gas with an initial temperature of \(127^{\circ} \mathrm{C}\) expand and, in the process, absorb 1200 J of heat and do 2100 J of work. What is the final temperature of the gas?

The process abc shown in the pV-diagram in Fig. E19.11 involves 0.0175 mole of an ideal gas. (a) What was the lowest temperature the gas reached in this process? Where did it occur? (b) How much work was done by or on the gas from a to b? From b to c? (c) If 215 J of heat was put into the gas during abc, how many of those joules went into internal energy?

A gas in a cylinder is held at a constant pressure of \(1.80\times10^5\mathrm{\ Pa}\) and is cooled and compressed from \(1.70\mathrm{\ m}^3\) to \(1.20\mathrm{\ m}^3\). The internal energy of the gas decreases by \(1.40\times10^5\mathrm{\ J}\). (a) Find the work done by the gas. (b) Find the absolute value \(|Q|\) of the heat flow into or out of the gas, and state the direction of the heat flow. (c) Does it matter whether the gas is ideal? Why or why not?

BIO Doughnuts: Breakfast of Champions! A typical doughnut contains 2.0 g of protein, 17.0 g of carbohydrates, and 7.0 g of fat. The average food energy values of these substances are for protein and carbohydrates and for fat. (a) During heavy exercise, an average person uses energy at a rate of How long would you have to exercise to work off one doughnut? (b) If the energy in the doughnut could somehow be converted into the kinetic energy of your body as a whole, how fast could you move after eating the doughnut? Take your mass to be 60 kg, and express your answer in and in

Boiling Water at High Pressure. When water is boiled at a pressure of 2.00 atm, the heat of vaporization is and the boiling point is At this pressure, 1.00 kg of water has a volume of and 1.00 kg of steam has a volume of (a) Compute the work done when 1.00 kg of steam is formed at this temperature. (b) Compute the increase in internal energy of the water

An ideal gas is taken from a to b on the pV-diagram shown in Fig. E19.15. During this process, 700 J of heat is added and the pressure doubles. (a) How much work is done by or on the gas? Explain. (b) How does the temperature of the gas at a compare to its temperature at b? Be specific. (c) How does the internal energy of the gas at a compare to the internal energy at b? Again, be specific and explain

A system is taken from state a to state b along the three paths shown in Fig. E19.16. (a) Along which path is the work done by the system the greatest? The least? (b) If U along which path is the absolute value of the heat transfer the greatest? For this path, is heat absorbed or liberated by the system?

A thermodynamic system undergoes a cyclic process as shown in Fig. E19.17. The cycle consists of two closed loops: I and II. (a) Over one complete cycle, does the system do positive or negative work? (b) In each of loops I and II, is the net work done by the system positive or negative? (c) Over one complete cycle, does heat flow into or out of the system? (d) In each of loops I and II, does heat flow into or out of the system?

During an isothermal compression of an ideal gas, 335 J of heat must be removed from the gas to maintain constant temperature. How much work is done by the gas during the process?

A cylinder contains 0.250 mol of carbon dioxide \(\left(\mathrm{CO}_{2}\right)\) gas at a temperature of \(27.0^{\circ} \mathrm{C}\). The cylinder is provided with a frictionless piston, which maintains a constant pressure of 1.00 atm on the gas. The gas is heated until its temperature increases to \(127.0^{\circ} \mathrm{C}\). Assume that the \(\left(\mathrm{CO}_{2}\right)\) may be treated as an ideal gas. (a) Draw a pV-diagram for this process. (b) How much work is done by the gas in this process? (c) On what is this work done? (d) What is the change in internal energy of the gas? (e) How much heat was supplied to the gas? (f) How much work would have been done if the pressure had been 0.50 atm?

A cylinder contains 0.0100 mol of helium at \(T=27.0^{\circ} \mathrm{C}\). (a) How much heat is needed to raise the temperature to \(67.0^{\circ} \mathrm{C}\) while keeping the volume constant? Draw a pV-diagram for this process. (b) If instead the pressure of the helium is kept constant, how much heat is needed to raise the temperature from \(27.0^{\circ} \mathrm{C}\) to \(67.0^{\circ} \mathrm{C}\)? Draw a pV-diagram for this process. (c) What accounts for the difference between your answers to parts (a) and (b)? In which case is more heat required? What becomes of the additional heat? (d) If the gas is ideal, what is the change in its internal energy in part (a)? In part (b)? How do the two answers compare? Why?

In an experiment to simulate conditions inside an automobile engine, 0.185 mol of air at a temperature of 780 K and a pressure of \(3.00 \times 10^{6} \mathrm{~Pa}\) is contained in a cylinder of volume \(40.0 \mathrm{~cm}^{3}\). Then 645 J of heat is transferred to the cylinder. (a) If the volume of the cylinder is constant while the heat is added, what is the final temperature of the air? Assume that the air is essentially nitrogen gas, and use the data in Table 19.1 even though the pressure is not low. Draw a pV-diagram for this process. (b) If instead the volume of the cylinder is allowed to increase while the pressure remains constant, find the final temperature of the air. Draw a pV-diagram for this process.

When a quantity of monatomic ideal gas expands at a constant pressure of the volume of the gas increases from to What is the change in the internal energy of the gas?

Heat Q flows into a monatomic ideal gas, and the volume increases while the pressure is kept constant. What fraction of the heat energy is used to do the expansion work of the gas?

Three moles of an ideal monatomic gas expands at a constant pressure of 2.50 atm; the volume of the gas changes from \(3.20\times10^{-2}\mathrm{\ m}^3\) to \(4.50\times10^{-2}\mathrm{\ m}^3\). (a) Calculate the initial and final temperatures of the gas. (b) Calculate the amount of work the gas does in expanding. (c) Calculate the amount of heat added to the gas. (d) Calculate the change in internal energy of the gas.

A cylinder with a movable piston contains 3.00 mol of gas (assumed to behave like an ideal gas). (a) The is heated at constant volume until 1557 J of heat have been added. Calculate the change in temperature. (b) Suppose the same amount of heat is added to the but this time the gas is allowed to expand while remaining at constant pressure. Calculate the temperature change. (c) In which case, (a) or (b), is the final internal energy of the higher? How do you know? What accounts for the difference between the two cases?

Propane gas \(C_{3}H_{8}\) behaves like an ideal gas with y = 1.127. Determine the molar heat capacity at constant volume and the molar heat capacity at constant pressure. Text Transcription: C_3H_8

The temperature of 0.150 mol of an ideal gas is held constant at \(77.0^{\circ} \mathrm{C}\) while its volume is reduced to 25.0% of its initial volume. The initial pressure of the gas is 1.25 atm. (a) Determine the work done by the gas. (b) What is the change in its internal energy? (c) Does the gas exchange heat with its surroundings? If so, how much? Does the gas absorb or liberate heat?

An experimenter adds 970 J of heat to 1.75 mol of an ideal gas to heat it from to at constant pressure. The gas does of work during the expansion. (a) Calculate the change in internal energy of the gas. (b) Calculate for the gas.

A monatomic ideal gas that is initially at a pressure of \(1.50 \times 10^{5} Pa\) and has a volume of \(0.0800 m^{3}\) is compressed adiabatically to a volume of \(0.0400 m^{3}\) (a) What is the final pressure? (b) How much work is done by the gas? (c) What is the ratio of the final temperature of the gas to its initial temperature? Is the gas heated or cooled by this compression? Text Transcription: 1.50 x 10^5 Pa 0.0800 m^3 0.0400 m^3

In an adiabatic process for an ideal gas, the pressure decreases. In this process does the internal energy of the gas increase or decrease? Explain your reasoning.

Two moles of carbon monoxide (CO) start at a pressure of 1.2 atm and a volume of 30 liters. The gas is then compressed adiabatically to this volume. Assume that the gas may be treated as ideal. What is the change in the internal energy of the gas? Does the internal energy increase or decrease? Does the temperature of the gas increase or decrease during this process? Explain.

The engine of a Ferrari F355 F1 sports car takes in air at and 1.00 atm and compresses it adiabatically to 0.0900 times the original volume. The air may be treated as an ideal gas with (a) Draw a pV-diagram for this process. (b) Find the final temperature and pressure

During an adiabatic expansion the temperature of 0.450 mol of argon (Ar) drops from \(50.0^{\circ} \mathrm{C} \text { to } 10.0^{\circ} \mathrm{C}\). The argon may be treated as an ideal gas. (a) Draw a pV-diagram for this process. (b) How much work does the gas do? (c) What is the change in internal energy of the gas? Text Transcription: 50.0^circ C to 10.0^circ C

A player bounces a basketball on the floor, compressing it to 80.0% of its original volume. The air (assume it is essentially gas) inside the ball is originally at a temperature of and a pressure of 2.00 atm. The balls inside diameter is 23.9 cm. (a) What temperature does the air in the ball reach at its maximum compression? Assume the compression is adiabatic and treat the gas as ideal. (b) By how much does the internal energy of the air change between the balls original state and its maximum compression?

On a warm summer day, a large mass of air (atmospheric pressure ) is heated by the ground to a temperature of and then begins to rise through the cooler surrounding air. (This can be treated approximately as an adiabatic process; why?) Calculate the temperature of the air mass when it has risen to a level at which atmospheric pressure is only Assume that air is an ideal gas, with (This rate of cooling for dry, rising air, corresponding to roughly per 100 m of altitude, is called the dry adiabatic lapse rate.)

A cylinder contains 0.100 mol of an ideal monatomic gas. Initially the gas is at a pressure of and occupies a volume of (a) Find the initial temperature of the gas in kelvins. (b) If the gas is allowed to expand to twice the initial volume, find the final temperature (in kelvins) and pressure of the gas if the expansion is (i) isothermal; (ii) isobaric; (iii) adiabatic.

One mole of ideal gas is slowly compressed to one-third of its original volume. In this compression, the work done on the gas has magnitude 600 J. For the gas, \(C_{p}=7 R / 2\). (a) If the process is isothermal, what is the heat flow Q for the gas? Does heat flow into or out of the gas? (b) If the process is isobaric, what is the change in internal energy of the gas? Does the internal energy increase or decrease?

CALC Figure P19.38 shows the pV-diagram for an isothermal expansion of 1.50 mol of an ideal gas, at a temperature of (a) What is the change in internal energy of the gas? Explain. (b) Calculate the work done by (or on) the gas and the heat absorbed (or released) by the gas during the expansion.

A quantity of air is taken from state a to state b along a path that is a straight line in the pV-diagram (Fig. P19.39). (a) In this process, does the temperature of the gas increase, decrease, or stay the same? Explain. (b) If and what is the work W done by the gas in this process? Assume that the gas may be treated as ideal.

One-half mole of an ideal gas is taken from state a to state c, as shown in Fig. P19.40. (a) Calculate the final temperature of the gas. (b) Calculate the work done on (or by) the gas as it moves from state a to state c. (c) Does heat leave the system or enter the system during this process? How much heat? Explain.

When a system is taken from state a to state b in Fig. P19.41 along the path acb, 90.0 J of heat flows into the system and 60.0 J of work is done by the system. (a) How much heat flows into the system along path adb if the work done by the system is 15.0 J? (b) When the system is returned from b to a along the curved path, the absolute value of the work done by the system is 35.0 J. Does the system absorb or liberate heat? How much heat? (c) If \(U_{a] = 0\) and \(U_{d} = 8.0 J\), find the heat absorbed in the processes ad and db. Text Transcription: U_a = 0 U_d = 8.0 J

A thermodynamic system is taken from state a to state c in Fig. P19.42 along either path abc or path adc. Along path abc, the work W done by the system is 450 J. Along path adc, W is 120 J. The internal energies of each of the four states shown in the figure are \(U_a=150\mathrm{\ J},\ U_b=240\mathrm{\ J},\ U_c=680\mathrm{\ J}\text{, and }U_d=330\mathrm{\ J}\). Calculate the heat flow Q for each of the four processes ab, bc, ad, and dc. In each process, does the system absorb or liberate heat?

A volume of air (assumed to be an ideal gas) is first cooled without changing its volume and then expanded without changing its pressure, as shown by the path abc in Fig. P19.43. (a) How does the final temperature of the gas compare with its initial temperature? (b) How much heat does the air exchange with its surroundings during the process abc? Does the air absorb heat or release heat during this process? Explain. (c) If the air instead expands from state a to state c by the straight-line path shown, how much heat does it exchange with its surroundings?

Three moles of argon gas (assumed to be an ideal gas) originally at a pressure of and a volume of are first heated and expanded at constant pressure to a volume of then heated at constant volume until the pressure reaches then cooled and compressed at constant pressure until the volume is again and finally cooled at constant volume until the pressure drops to its original value of (a) Draw the pV- diagram for this cycle. (b) Calculate the total work done by (or on) the gas during the cycle. (c) Calculate the net heat exchanged with the surroundings. Does the gas gain or lose heat overall?

Two moles of an ideal monatomic gas go through the cycle abc. For the complete cycle, 800 J of heat flows out of the gas. Process ab is at constant pressure, and process bc is at constant volume. States a and b have temperatures and (a) Sketch the pV-diagram for the cycle. (b) What is the work W for the process ca?

Three moles of an ideal gas are taken around the cycle acb shown in Fig. P19.46. For this gas, \(C_{p}=29.1 \mathrm{~J} / \mathrm{mol} \cdot \mathrm{K}\). Process ac is at constant pressure, process ba is at constant volume, and process cb is adiabatic. The temperatures of the gas in states a, c, and b are \(T_{a}=300 \mathrm{~K}, T_{c}=492 \mathrm{~K} \text {, and } T_{b}=600 \mathrm{~K}\). Calculate the total work W for the cycle.

Figure P19.47 shows a pV-diagram for 0.0040 mole of ideal gas. The temperature of the gas does not change during segment bc. (a) What volume does this gas occupy at point c? (b) Find the temperature of the gas at points a, b, and c. (c) How much heat went into or out of the gas during segments ab, ca, and bc? Indicate whether the heat has gone into or out of the gas. (d) Find the change in the internal energy of this hydrogen during segments ab, bc, and ca. Indicate whether the internal energy increased or decreased during each of these segments.

The graph in Fig. P19.48 shows a pV-diagram for 3.25 moles of ideal helium (He) gas. Part ca of this process is isothermal. (a) Find the pressure of the He at point a. (b) Find the temperature of the He at points a, b, and c. (c) How much heat entered or left the He during segments ab, bc, and ca? In each segment, did the heat enter or leave? (d) By how much did the internal energy of the He change from a to b, from b to c, and from c to a? Indicate whether this energy increased or decreased

(a) One-third of a mole of He gas is taken along the path abc shown as the solid line in Fig. P19.49. Assume that the gas may be treated as ideal. How much heat is transferred into or out of the gas? (b) If the gas instead went from state a to state c along the horizontal dashed line in Fig. P19.49, how much heat would be transferred into or out of the gas? (c) How does Q in part (b) compare with Q in part (a)? Explain.

Two moles of helium are initially at a temperature of 27.0C and occupy a volume of The helium first expands at constant pressure until its volume has doubled. Then it expands adiabatically until the temperature returns to its initial value. Assume that the helium can be treated as an ideal gas. (a) Draw a diagram of the process in the pV-plane. (b) What is the total heat supplied to the helium in the process? (c) What is the total change in internal energy of the helium? (d) What is the total work done by the helium? (e) What is the final volume of the helium?

Starting with 2.50 mol of gas (assumed to be ideal) in a cylinder at 1.00 atm and a chemist first heats the gas at constant volume, adding of heat, then continues heating and allows the gas to expand at constant pressure to twice its original volume. (a) Calculate the final temperature of the gas. (b) Calculate the amount of work done by the gas. (c) Calculate the amount of heat added to the gas while it was expanding. (d) Calculate the change in internal energy of the gas for the whole process.

Nitrogen gas in an expandable container is cooled from to with the pressure held constant at The total heat liberated by the gas is Assume that the gas may be treated as ideal. (a) Find the number of moles of gas. (b) Find the change in internal energy of the gas. (c) Find the work done by the gas. (d) How much heat would be liberated by the gas for the same temperature change if the volume were constant?

In a certain process, \(2.15 \times 10^{5} J\) of heat is liberated by a system, and at the same time the system contracts under a constant external pressure of \(9.50 \times 10^{5} Pa\). The internal energy of the system is the same at the beginning and end of the process. Find the change in volume of the system. (The system is not an ideal gas.) Text Transcription: 2.15 x 10^5 J 9.50 x 10^5 Pa

CALC A cylinder with a frictionless, movable piston like that shown in Fig. 19.5 contains a quantity of helium gas. Initially the gas is at a pressure of has a temperature of 300 K, and occupies a volume of 1.50 L. The gas then undergoes two processes. In the first, the gas is heated and the piston is allowed to move to keep the temperature equal to 300 K. This continues until the pressure reaches In the second process, the gas is compressed at constant pressure until it returns to its original volume of 1.50 L. Assume that the gas may be treated as ideal. (a) In a pV-diagram, show both processes. (b) Find the volume of the gas at the end of the first process, and find the pressure and temperature at the end of the second process. (c) Find the total work done by the gas during both processes. (d) What would you have to do to the gas to return it to its original pressure and temperature?

A Thermodynamic Process in a Liquid. A chemical engineer is studying the properties of liquid methanol \(\left(\mathrm{CH}_{3} \mathrm{OH}\right)\). She uses a steel cylinder with a cross-sectional area of \(0.0200 \mathrm{~m}^{2}\) and containing \(1.20 \times 10^{-2} \mathrm{~m}^{3}\) of methanol. The cylinder is equipped with a tightly fitting piston that supports a load of \(3.00 \times 10^{4} \mathrm{~N}\). The temperature of the system is increased from \(20.0^{\circ} \mathrm{C} \text { to } 50.0^{\circ} \mathrm{C}\). For methanol, the coefficient of volume expansion is \(1.20 \times 10^{-3} \mathrm{~K}^{-1}\), the density is \(791 \mathrm{~kg} / \mathrm{m}^{3}\), and the specific heat at constant pressure is \(c_{p}=2.51 \times 10^{3} \mathrm{~J} / \mathrm{kg} \cdot \mathrm{K}\) You can ignore the expansion of the steel cylinder. Find (a) the increase in volume of the methanol; (b) the mechanical work done by the methanol against the \(3.00 \times 10^{4} \mathrm{~N}\) force; (c) the amount of heat added to the methanol; (d) the change in internal energy of the methanol. (e) Based on your results, explain whether there is any substantial difference between the specific heats \(c_p\) (at constant pressure) and \(c_v\) (at constant volume) for methanol under these conditions.

CP A Thermodynamic Process in a Solid. A cube of copper 2.00 cm on a side is suspended by a string. (The physical properties of copper are given in Tables 14.1, 17.2, and 17.3.) The cube is heated with a burner from to The air surrounding the cube is at atmospheric pressure Find (a) the increase in volume of the cube; (b) the mechanical work done by the cube to expand against the pressure of the surrounding air; (c) the amount of heat added to the cube; (d) the change in internal energy of the cube. (e) Based on your results, explain whether there is any substantial difference between the specific heats (at constant pressure) and (at constant volume) for copper under these conditions.

BIO A Thermodynamic Process in an Insect. The African bombardier beetle (Stenaptinus insignis) can emit a jet of defensive spray from the movable tip of its abdomen (Fig. P19.57). The beetles body has reservoirs of two different chemicals; when the beetle is disturbed, these chemicals are combined in a reaction chamber, producing a compound that is warmed from to by the heat of reaction. The high pressure produced allows the compound to be sprayed out at speeds up to scaring away predators of all kinds. (The beetle shown in the figure is 2 cm long.) Calculate the heat of reaction of the two chemicals (in ). Assume that the specific heat of the two chemicals and the spray is the same as that of water, and that the initial temperature of the chemicals is

High-Altitude Research. A large research balloon containing \(2.00\times10^3\ m^3\) of helium gas at 1.00 atm and a temperature of \(15.0^{\circ}C\) rises rapidly from ground level to an altitude at which the atmospheric pressure is only 0.900 atm (Fig. P19.58). Assume the helium behaves like an ideal gas and the balloon’s ascent is too rapid to permit much heat exchange with the surrounding air. (a) Calculate the volume of the gas at the higher altitude. (b) Calculate the temperature of the gas at the higher altitude. (c) What is the change in internal energy of the helium as the balloon rises to the higher altitude?

Chinook. During certain seasons strong winds called chinooks blow from the west across the eastern slopes of the Rockies and downhill into Denver and nearby areas. Although the mountains are cool, the wind in Denver is very hot; within a few minutes after the chinook wind arrives, the temperature can climb (chinook is a Native American word meaning snow eater). Similar winds occur in the Alps (called foehns) and in southern California (called Santa Anas). (a) Explain why the temperature of the chinook wind rises as it descends the slopes. Why is it important that the wind be fast moving? (b) Suppose a strong wind is blowing toward Denver (elevation 1630 m) from Grays Peak (80 km west of Denver, at an elevation of 4350 m), where the air pressure is and the air temperature is The temperature and pressure in Denver before the wind arrives are and By how many Celsius degrees will the temperature in Denver rise when the chinook arrives?

A certain ideal gas has molar heat capacity at constant volume \(C_{V}\). A sample of this gas initially occupies a volume \(V_{0}\) at pressure \(p_{0}\) and absolute temperature \(T_{0}\). The gas expands isobarically to a volume \(2V_{0}\) and then expands further adiabatically to a final volume \(4V_{0}\). (a) Draw a pV-diagram for this sequence of processes. (b) Compute the total work done by the gas for this sequence of processes. (c) Find the final temperature of the gas. (d) Find the absolute value \(|Q|\) of the total heat flow into or out of the gas for this sequence of processes, and state the direction of heat flow

An air pump has a cylinder 0.250 m long with a movable piston. The pump is used to compress air from the atmosphere (at absolute pressure ) into a very large tank at gauge pressure. (For air, ) (a) The piston begins the compression stroke at the open end of the cylinder. How far down the length of the cylinder has the piston moved when air first begins to flow from the cylinder into the tank? Assume that the compression is adiabatic. (b) If the air is taken into the pump at what is the temperature of the compressed air? (c) How much work does the pump do in putting 20.0 mol of air into the tank?

Engine Turbochargers and Intercoolers. The power output of an automobile engine is directly proportional to the mass of air that can be forced into the volume of the engine's cylinders to react chemically with gasoline. Many cars have a turbocharger, which compresses the air before it enters the engine, giving a greater mass of air per volume. This rapid, essentially adiabatic compression also heats the air. To compress it further, the air then passes through an intercooler in which the air exchanges heat with its surroundings at essentially constant pressure. The air is then drawn into the cylinders. In a typical installation, air is taken into the turbocharger at atmospheric pressure \(\left(1.01\times10^5\mathrm{\ Pa}\right)\), density \(\rho=1.23\mathrm{\ kg}/\mathrm{m}^3\) and temperature \(15.0^{\circ} \mathrm{C}\). It is compressed adiabatically to \(1.45\times10^5\mathrm{\ Pa}\). In the intercooler, the air is cooled to the original temperature of \(15.0^{\circ} \mathrm{C}\) at a constant pressure of \(1.45\times10^5\mathrm{\ Pa}\). (a) Draw a pV-diagram for this sequence of processes. (b) If the volume of one of the engine’s cylinders is \(575\mathrm{\ cm}^3\), what mass of air exiting from the intercooler will fill the cylinder at \(1.45\times10^5\mathrm{\ Pa}\)? Compared to the power output of an engine that takes in air at \(1.01\times10^5\mathrm{\ Pa}\) at \(15.0^{\circ} \mathrm{C}\), what percentage increase in power is obtained by using the turbocharger and intercooler? (c) If the intercooler is not used, what mass of air exiting from the turbocharger will fill the cylinder at \(1.45\times10^5\mathrm{\ Pa}\)? Compared to the power output of an engine that takes in air at \(1.01\times10^5\mathrm{\ Pa}\) at \(15.0^{\circ} \mathrm{C}\), what percentage increase in power is obtained by using the turbocharger alone?

A monatomic ideal gas expands slowly to twice its original volume, doing 300 J of work in the process. Find the heat added to the gas and the change in internal energy of the gas if the process is (a) isothermal; (b) adiabatic; (c) isobaric.

CALC A cylinder with a piston contains 0.250 mol of oxygen at and 355 K. The oxygen may be treated as an ideal gas. The gas first expands isobarically to twice its original volume. It is then compressed isothermally back to its original volume, and finally it is cooled isochorically to its original pressure. (a) Show the series of processes on a pV-diagram. (b) Compute the temperature during the isothermal compression. (c) Compute the maximum pressure. (d) Compute the total work done by the piston on the gas during the series of processes.

Use the conditions and processes of Problem 19.64 to compute (a) the work done by the gas, the heat added to it, and its internal energy change during the initial expansion; (b) the work done, the heat added, and the internal energy change during the final cooling; (c) the internal energy change during the isothermal compression.

CALC A cylinder with a piston contains 0.150 mol of nitrogen at and 300 K. The nitrogen may be treated as an ideal gas. The gas is first compressed isobarically to half its original volume. It then expands adiabatically back to its original volume, and finally it is heated isochorically to its original pressure. (a) Show the series of processes in a pV-diagram. (b) Compute the temperatures at the beginning and end of the adiabatic expansion. (c) Compute the minimum pressure.

Use the conditions and processes of Problem 19.66 to compute (a) the work done by the gas, the heat added to it, and its internal energy change during the initial compression; (b) the work done by the gas, the heat added to it, and its internal energy change during the adiabatic expansion; (c) the work done, the heat added, and the internal energy change during the final heating.

Comparing Thermodynamic Processes. In a cylinder, 1.20 mol of an ideal monatomic gas, initially at \(3.60\times10^5\mathrm{\ Pa}\) and 300 K, expands until its volume triples. Compute the work done by the gas if the expansion is (a) isothermal; (b) adiabatic; (c) isobaric. (d) Show each process in a pV-diagram. In which case is the absolute value of the work done by the gas greatest? Least? (e) In which case is the absolute value of the heat transfer greatest? Least? (f) In which case is the absolute value of the change in internal energy of the gas greatest? Least?

CP Oscillations of a Piston. A vertical cylinder of radius r contains a quantity of ideal gas and is fitted with a piston with mass m that is free to move (Fig. P19.69). The piston and the walls of the cylinder are frictionless, and the entire cylinder is placed in a constant-temperature bath. The outside air pressure is In equilibrium, the piston sits at a height h above the bottom of the cylinder. (a) Find the absolute pressure of the gas trapped below the piston when in equilibrium. (b) The piston is pulled up by a small distance and released. Find the net force acting on the piston when its base is a distance above the bottom of the cylinder, where y is much less than h. (c) After the piston is displaced from equilibrium and released, it oscillates up and down. Find the frequency of these small oscillations. If the displacement is not small, are the oscillations simple harmonic? How can you tell?

Problem 1DQ For the following processes, is the work done by the system (defined as the expanding or contracting gas) on the environment positive or negative? (a) expansion of the burned gasoline–air mixture in the cylinder of an automobile engine; (b) opening a bottle of champagne; (c) filling a scuba tank with compressed air; (d) partial crumpling of a sealed, empty water bottle as you drive from the mountains down to sea level.

Problem 1E Two moles of an ideal gas are heated at constant pressure from T = 27o C to T = 107o C. (a) Draw a pV-diagram for this process. (b) Calculate the work done by the gas.

Problem 2DQ It is not correct to say that a body contains a certain amount of heat, yet a body can transfer heat to another body. How can a body give away something it does not have in the first place?

Problem 2E Six moles of an ideal gas are in a cylinder fitted at one end with a movable piston. The initial temperature of the gas is 27.0o C and the pressure is constant. As part of a machine design project, calculate the final temperature of the gas after it has done 2.40 X 103 J of work.

Problem 3DQ In which situation must you do more work: inflating a balloon at sea level or inflating the same balloon to the same volume at the summit of Mt. McKinley? Explain in terms of pressure and volume change.

Problem 3E CALC Two moles of an ideal gas are compressed in a cylinder at a constant temperature of 65.0o C until the original pressure has tripled. (a) Sketch a pV-diagram for this process. (b) Calculate the amount of work done.

Problem 4DQ If you are told the initial and final states of a system and the associated change in internal energy, can you determine whether the internal energy change was due to work or to heat transfer? Explain.

BIO Work Done by the Lungs. The graph in Fig. E19.4 shows a pV diagram of the air in a human lung when a person is inhaling and then exhaling a deep breath. Such graphs, obtained in clinical practice, are normally somewhat curved, but we have modeled one as a set of straight lines of the same general shape. (Important: The pressure shown is the gauge pressure, not the absolute pressure.) (a) How many joules of net work does this person’s lung do during one complete breath? (b) The process illustrated here is somewhat different from those we have been studying, because the pressure change is due to changes in the amount of gas in the lung, not to temperature changes. (Think of your own breathing. Your lungs do not expand because they’ve gotten hot.) If the temperature of the air in the lung remains a reasonable \(20^{\circ} \mathrm{C}\), what is the maximum number of moles in this person’s lung during a breath? Equation Transcription: Text Transcription: 20degC

Problem 5DQ Discuss the application of the first law of thermodynamics to a mountaineer who eats food, gets warm and perspires a lot during a climb, and does a lot of mechanical work in raising herself to the summit. The mountaineer also gets warm during the descent. Is the source of this energy the same as the source during the ascent?

Problem 5E During the time 0.305 mol of an ideal gas undergoes an isothermal compression at 22.0°C. 468 J of work is done on it by the surroundings. (a) If the final pressure is 1.76 atm, what was the initial pressure? (b) Sketch a pV-diagram for the process.

Problem 6DQ When ice melts at 0o C, its volume decreases. Is the internal energy change greater than, less than, or equal to the heat added? How can you tell?

Problem 6E A gas undergoes two processes. In the first, the volume remains constant at 0.200 m3 and the pressure increases from 2.00 X 105 Pa to 5.00 X 105 Pa. The second process is a compression to a volume of 0.120 m3 at a constant pressure of 5.00 X 105 Pa. (a) In a pV-diagram, show both processes. (b) Find the total work done by the gas during both processes.

Problem 7DQ You hold an inflated balloon over a hot-air vent in your house and watch it slowly expand. You then remove it and let it cool back to room temperature. During the expansion, which was larger: the heat added to the balloon or the work done by the air inside it? Explain. (Assume that air is an ideal gas.) Once the balloon has returned to room temperature, how does the net heat gained or lost by the air inside it compare to the net work done on or by the surrounding air?

Work Done in a Cyclic Process. (a) In Fig. 19.7a, consider the closed loop \(1 \rightarrow 3 \rightarrow 2 \rightarrow 4 \rightarrow 1\). This is a cyclic process in which the initial and final states are the same. Find the total work done by the system in this cyclic process, and show that it is equal to the area enclosed by the loop. (b) How is the work done for the process in part (a) related to the work done if the loop is traversed in the opposite direction, \(1 \rightarrow 4 \rightarrow 2 \rightarrow 3 \rightarrow 1\)? Explain. Equation Transcription: Text Transcription: 1-3-2-4-1 1-4-2-3-1

Problem 8DQ You bake chocolate chip cookies and put them, still warm, in a container with a loose (not airtight) lid. What kind of process does the air inside the container undergo as the cookies gradually cool to room temperature (isothermal, isochoric, adiabatic, isobaric, or some combination)? Explain.

Figure E19.8 shows a \(p V \text {-diagram }\) for an ideal gas in which its absolute temperature at is one-fourth of its absolute temperature at . (a) What volume does this gas occupy at point? (b) How many joules of work was done by or on the gas in this process? Was it done by or on the gas? (c) Did the internal energy of the gas increase or decrease from to ? How do you know? (d) Did heat enter or leave the gas from to ? How do you know? Equation Transcription: Text Transcription: pV-diagram p(atm) V(L)

Problem 9DQ Imagine a gas made up entirely of negatively charged electrons. Like charges repel, so the electrons exert repulsive forces on each other. Would you expect that the temperature of such a gas would rise, fall, or stay the same in a free expansion? Why?

Problem 9E A gas in a cylinder expands from a volume of 0.110 m3 to 0.320 m3. Heat flows into the gas just rapidly enough to keep the pressure constant at 1.65 X 105 Pa during the expansion. The total heat added is 1.15 X 105 J. (a) Find the work done by the gas. (b) Find the change in internal energy of the gas. (c) Does it matter whether the gas is ideal? Why or why not?

There are a few materials that contract when their temperature is increased, such as water between 0\(^\circ\)C and 4\(^\circ\)C. Would you expect Cp, for such materials to be greater or less than CV? Explain?

Problem 10E Five moles of an ideal monatomic gas with an initial temperature of 127°C expand and, in the process, absorb 1200 J of heat and do 2100 J of work. What is the final temperature of the gas?

The process \(a b c\) shown in the \(p V \text {-diagram }\) in Fig. E19.11 involves 0.0175 mole of an ideal gas. (a) What was the lowest temperature the gas reached in this process? Where did it occur? (b) How much work was done by or on the gas from to? From to ? (c) If 215 J of heat was put into the gas during \(a b c\), how many of those joules went into internal energy? Equation Transcription: Text Transcription: abc pV-diagram p(atm) V(L)

Problem 12DQ An ideal gas expands while the pressure is kept constant. During this process, does heat flow into the gas or out of the gas? Justify your answer.

A gas in a cylinder is held at a constant pressure of 1.80 X 105 Pa and is cooled and compressed from 1.70 m3 to 1.20 m3. The internal energy of the gas decreases by 1.40 X 105 J. (a) Find the work done by the gas. (b) Find the absolute value of the heat flow, |Q|, into or out of the gas, and state the direction of the heat flow. (c) Does it matter whether the gas is ideal? Why or why not?

Problem 13DQ A liquid is irregularly stirred in a well-insulated container and thereby undergoes a rise in temperature. Regard the liquid as the system. Has heat been transferred? How can you tell? Has work been done? How can you tell? Why is it important that the stirring is irregular? What is the sign of ?U? How can you tell?

Problem 13E Doughnuts: Breakfast of Champions! A typical doughnut contains 2.0 g of protein, 17.0 g of carbohydrates, and 7.0 g of fat. The average food energy values of these substances are 4.0 kcal/g for protein and carbohydrates and 9.0 kcal/g for fat. (a) During heavy exercise, an average person uses energy at a rate of 510 kcal/h. How long would you have to exercise to “work off” one doughnut? (b) If the energy in the doughnut could somehow be converted into the kinetic energy of your body as a whole, how fast could you move after eating the doughnut? Take your mass to be 60 kg, and express your answer in m/s and in km/h.

When you use a hand pump to inflate the tires of your bicycle, the pump gets warm after a while. Why? What happens to the temperature of the air in the pump as you compress it? Why does this happen? When you raise the pump handle to draw outside air into the pump, what happens to the temperature of the air taken in? Again, why does this happen?

Problem 14E Boiling Water at High Pressure. When water is boiled at a pressure of 2.00 atm, the heat of vaporization is 2.20 X 106 J/kg and the boiling point is 120o C. At this pressure, 1.00 kg of water has a volume of 1.00 X 10-3 m3, and 1.00 kg of steam has a volume of 0.824 m3. (a) Compute the work done when 1.00 kg of steam is formed at this temperature. (b) Compute the increase in internal energy of the water.

Problem 15DQ In the carburetor of an aircraft or automobile engine, air flows through a relatively small aperture and then expands. In cool, foggy weather, ice sometimes forms in this aperture even though the outside air temperature is above freezing. Why?

An ideal gas is taken from a to b on the \(p V \text {-diagram }\) shown in Fig. E19.15. During this process, 700 J of heat is added and the pressure doubles. (a) How much work is done by or on the gas? Explain. (b) How does the temperature of the gas at compare to its temperature at ? Be specific. (c) How does the internal energy of the gas at compare to the internal energy at ? Again, be specific and explain. Equation Transcription: Text Transcription: pV-diagram p(kPa) V(m^3)

Problem 16DQ On a sunny day, large “bubbles” of air form on the sun-warmed earth, gradually expand, and finally break free to rise through the atmosphere. Soaring birds and glider pilots are fond of using these “thermals” to gain altitude easily. This expansion is essentially an adiabatic process. Why?

A system is taken from state to state along the three paths shown in Fig. E19.16. (a) Along which path is the work done by the system the greatest? The least? (b) If \(U_{b}>U_{a}\), along which path is the absolute value \(|Q|\) of the heat transfer the greatest? For this path, is heat absorbed or liberated by the system? Equation Transcription: Text Transcription: U_b>U_a |Q|

Problem 17DQ The prevailing winds on the Hawaiian island of Kauai blow from the northeast. The winds cool as they go up the slope of Mt. Waialeale (elevation 1523 m), causing water vapor to con-dense and rain to fall. There is much more precipitation at the summit than at the base of the mountain. In fact, Mt. Waialeale is the rainiest spot on earth, averaging 11.7 m of rainfall a year. But what makes the winds cool?

A thermodynamic system undergoes a cyclic process as shown in Fig. E19.17. The cycle consists of two closed loops: I and II. (a) Over one complete cycle, does the system do positive or negative work? (b) In each of loops I and II, is the net work done by the system positive or negative? (c) Over one complete cycle, does heat flow into or out of the system? (d) In each of loops I and II, does heat flow into or out of the system?

Problem 18DQ Applying the same considerations as in Question Q19.17, explain why the island of Niihau, a few kilometers to the south-west of Kauai, is almost a desert and farms there need to be irrigated. Q19.17 The prevailing winds on the Hawaiian island of Kauai blow from the northeast. The winds cool as they go up the slope of Mt. Waialeale (elevation 1523 m), causing water vapor to con-dense and rain to fall. There is much more precipitation at the summit than at the base of the mountain. In fact, Mt. Waialeale is the rainiest spot on earth, averaging 11.7 m of rainfall a year. But what makes the winds cool?

Problem 18E During an isothermal compression of an ideal gas, 335 J of heat must be removed from the gas to maintain constant temperature. How much work is done by the gas during the process?

Problem 19DQ In a constant-volume process, dU = nCVdT. But in a constant-pressure process, it is not true that dU = nCpdT. Why not?

Problem 19E A cylinder contains 0.250 mol of carbon dioxide (CO2) gas at a temperature of 27.0o C. The cylinder is provided with a frictionless piston, which maintains a constant pressure of 1.00 atm on the gas. The gas is heated until its temperature increases to 127.0o C. Assume that the CO2 may be treated as an ideal gas. (a) Draw a pV-diagram for this process. (b) How much work is done by the gas in this process? (c) On what is this work done? (d) What is the change in internal energy of the gas? (e) How much heat was supplied to the gas? (f) How much work would have been done if the pressure had been 0.50 atm?

Problem 20DQ When a gas surrounded by air is compressed adiabatically, its temperature rises even though there is no heat input to the gas. Where does the energy come from to raise the temperature?

Problem 21DQ When a gas expands adiabatically, it does work on its surroundings. But if there is no heat input to the gas, where does the energy come from to do the work?

When a gas expands adiabatically, it does work on its surroundings. But if there is no heat input to the gas, where does the energy come from to do the work?

Problem 20E A cylinder contains 0.0100 mol of helium at T = 27.0o C. (a) How much heat is needed to raise the temperature to 67.0o C while keeping the volume constant? Draw a pV-diagram for this process. (b) If instead the pressure of the helium is kept constant, how much heat is needed to raise the temperature from 27.0o C to 67.0o C? Draw a pV-diagram for this process. (c) What accounts for the difference between your answers to parts (a) and (b)? In which case is more heat required? What becomes of the additional heat? (d) If the gas is ideal, what is the change in its internal energy in part (a)? In part (b)? How do the two answers compare? Why?

Problem 22DQ The gas used in separating the two uranium isotopes 235U and 238U has the formula UF6. If you added heat at equal rates to a mole of UF6 gas and a mole of H2 gas, which one’s temperature would you expect to rise faster? Explain.

Problem 22E When a quantity of monatomic ideal gas expands at a constant pressure of 4.00 X 104 Pa, the volume of the gas increases from 2.00 X 10-3 m3 to 8.00 X 10-3 m3. What is the change in the internal energy of the gas?

Heat Q flows into a monatomic ideal gas, and the volume increases while the pressure is kept constant. What fraction of the heat energy is used to do the expansion work of the gas?

Problem 24E Three moles of an ideal monatomic gas expands at a constant pressure of 2.50 atm; the volume of the gas changes from 3.20 X 10-2 m3 to 4.50 X 10-2 m3. Calculate (a) the initial and final temperatures of the gas; (b) the amount of work the gas does in expanding; (c) the amount of heat added to the gas; (d) the change in internal energy of the gas.

Problem 25E A cylinder with a movable piston contains 3.00 mol of N2 gas (assumed to behave like an ideal gas). (a) The N2 is heated at constant volume until 1557 J of heat have been added. Calculate the change in temperature. (b) Suppose the same amount of heat is added to the N2, but this time the gas is allowed to expand while remaining at constant pressure. Calculate the temperature change. (c) In which case (a) or (b), is the final internal energy of the N2 higher? how do you know? What accounts for the difference between the two cases.

Propane gas \(\left(\mathrm{C}_{3} \mathrm{H}_{8}\right)\) behaves like an ideal gas with \(\gamma=1.127\). Determine the molar heat capacity at constant volume and the molar heat capacity at constant pressure.

Problem 27E CALC The temperature of 0.150 mol of an ideal gas is held constant at 77.0o C while its volume is reduced to 25.0% of its initial volume. The initial pressure of the gas is 1.25 atm. (a) Determine the work done by the gas. (b) What is the change in its internal energy? (c) Does the gas exchange heat with its surroundings? If so, how much? Does the gas absorb or liberate heat?

Problem 28E An experimenter adds 970 J of heat to 1.75 mol of an ideal gas to heat it from 10.0o C to 25.0o C at constant pressure. The gas does + 223 J of work during the expansion. (a) Calculate the change in internal energy of the gas. (b) Calculate ? for the gas.

Problem 29E A monatomic ideal gas that is initially at 1.50 X 105 Pa and has a volume of 0.0800 m3 is compressed adiabatically to a volume of 0.0400 m3. (a) What is the final pressure? (b) How much work is done by the gas? (c) What is the ratio of the final temperature of the gas to its initial temperature? Is the gas heated or cooled by this compression?

Problem 30E In an adiabatic process for an ideal gas, the pressure decreases. In this process does the internal energy of the gas increase or decrease? Explain your reasoning.

Two moles of carbon monoxide (CO) start at a pressure of 1.2 atm and a volume of 30 liters. The gas is then compressed adiabatically to \(\frac{1}{3}\) this volume. Assume that the gas may be treated as ideal. What is the change in the internal energy of the gas? Does the internal energy increase or decrease? Does the temperature of the gas increase or decrease during this process? Explain. Equation Transcription: Text Transcription: 1/3

Problem 32E The engine of a Ferrari F355 F1 sports car takes in air at 20.0o C and 1.00 atm and compresses it adiabatically to 0.0900 times the original volume. The air may be treated as an ideal gas with ? = 1.40. (a) Draw a pV-diagram for this process. (b) Find the final temperature and pressure.

Problem 33E During an adiabatic expansion the temperature of 0.450 mol of argon (Ar) drops from 66.0o C to 10.0o C. The argon may be treated as an ideal gas. (a) Draw a pV-diagram for this process. (b) How much work does the gas do? (c) What is the change in internal energy of the gas?

Problem 34E A player bounces a basketball on the floor, compressing it to 80.0% of its original volume. The air (assume it is essentially N2 gas) inside the ball is originally at 20.0o C and 2.00 atm. The ball’s inside diameter is 23.9 cm. (a) What temperature does the air in the ball reach at its maximum compression? Assume the compression is adiabatic and treat the gas as ideal. (b) By how much does the internal energy of the air change between the ball’s original state and its maximum compression?

Problem 35E On a warm summer day, a large mass of air (atmospheric pressure 1.01 X 105 Pa) is heated by the ground to 26.0o C and then begins to rise through the cooler surrounding air. (This can be treated approximately as an adiabatic process; why?) Calculate the temperature of the air mass when it has risen to a level at which atmospheric pressure is only 0.850 X 105 Pa. Assume that air is an ideal gas, with ? = 1.40. (This rate of cooling for dry, rising air, corresponding to roughly 1 Co per 100 m of altitude, is called the dry adiabatic lapse rate.)

Problem 36E A cylinder contains 0.100 mol of an ideal monatomic gas. Initially the gas is at 1.00 X 105 Pa and occupies a volume of 2.50 X 10-3 m3. (a) Find the initial temperature of the gas in kelvins. (b) If the gas is allowed to expand to twice the initial volume, find the final temperature (in kelvins) a

Problem 37P One mole of ideal gas is slowly compressed to one-third of its original volume. In this compression, the work done on the gas has magnitude 600 J. For the gas, Cp = 7R/2. (a) If the process is isothermal, what is the heat flow Q for the gas? Does heat flow into or out of the gas? (b) If the process is isobaric, what is the change in internal energy of the gas? Does the internal energy increase or decrease?

CALC Figure P19.38 shows the \(p V \text {-diagram }\) for an isothermal expansion of 1.50 mol of an ideal gas, at a temperature of \(15.0^{\circ} \mathrm{C}). (a) What is the change in internal energy of the gas? Explain. (b) Calculate the work done by (or on) the gas and the heat absorbed (or released) by the gas during the expansion. Equation Transcription: Text Transcription: pV-diagram 15.0degC p(Pa) V(m^3)

A quantity of air is taken from state to state along a path that is a straight line in the \(p V \text {-diagram }\) (Fig. P19.39). (a) In this process, does the temperature of the gas increase, decrease, or stay the same? Explain. (b) If \(V_{a}=0.0700 \mathrm{~m}^{3}\), \(V_{b}=0.1100 \mathrm{~m}^{3}\), \(P_{a}=1.00 \times 10^{5}\) Pa, \(P_{b}=1.40 \times 10^{5}\) Pa, what is the work done by the gas in this process? Assume that the gas may be treated as ideal. Equation Transcription: Text Transcription: pV-diagram V_a=0.0700 m^3 V_b=0.1100 m^3 P_a=1.00x10^5 P_b=1.40x10^5 Pb Pa V_a V_b

One-half mole of an ideal gas is taken from state to state , as shown in Fig. P19.40. (a) Calculate the final temperature of the gas. (b) Calculate the work done on (or by) the gas as it moves from state to state . (c) Does heat leave the system or enter the system during this process? How much heat? Explain. Equation Transcription: Text Transcription: p(Pa) V(m^3)

When a system is taken from state to state in Fig. P19.41 along the path \(a c b\), 90.0 J of heat flows into the system and 60.0 J of work is done by the system. (a) How much heat flows into the system along path \(a d b\) if the work done by the system is 15.0 J? (b) When the system is returned from to along the curved path, the absolute value of the work done by the system is 35.0 J. Does the system absorb or liberate heat? How much heat? (c) If \(U_{a}=0\) and \(U_{d}=8.0 \mathrm{~J}\), find the heat absorbed in the processes \(a d\) and \(d b\). Equation Transcription: Text Transcription: acb adb U_a=0 U_d=8.0 J ad db

A thermodynamic system is taken from state to state in Fig. P19.42 along either path \(a b c\) or path \(a d c\). Along path \(a b c\), the work done by the system is 450 J. Along path \(a d c\), is 120 J. The internal energies of each of the four states shown in the figure are \(U_{a}=150 \mathrm{~J}\), \(U_{b}=240 \mathrm{~J}\), \(U_{c}=680 \mathrm{~J}\) and \(U_{d}=330 \mathrm{~J}\). Calculate the heat flow for each of the four processes \(a b, b c, a d\), and \(d c\). In each process, does the system absorb or liberate heat? Equation Transcription: Text Transcription: abc adc abc adc U_a=150 J U_b=240 J U_c=680 J U_d=330 J ab,bc,ad dc

A volume of air (assumed to be an ideal gas) is first cooled without changing its volume and then expanded without changing its pressure, as shown by the path \(a b c\) in Fig. P19.43. (a) How does the final temperature of the gas compare with its initial temperature? (b) How much heat does the air exchange with its surroundings during the process \(a b c\)? Does the air absorb heat or release heat during this process? Explain. (c) If the air instead expands from state to state by the straight-line path shown, how much heat does it exchange with its surroundings? Equation Transcription: Text Transcription: abc abc p(Pa) 3.0x10^5 2.0x10^5 1.0x10^5 V(m^3)

Problem 44P Three moles of argon gas (assumed to be an ideal gas) originally at 1.50 X 104 Pa and a volume of 0.0280 m3 are first heated and expanded at constant pressure to a volume of 0.0435 m3, then heated at constant volume until the pressure reaches 3.50 X 104 Pa, then cooled and compressed at constant pressure until the volume is again 0.0280 m3, and finally cooled at constant volume until the pressure drops to its original value of 1.50 X 104 Pa. (a) Draw the pV-diagram for this cycle. (b) Calculate the total work done by (or on) the gas during the cycle. (c) Calculate the net heat exchanged with the surroundings. Does the gas gain or lose heat overall?

Problem 45P Two moles of an ideal monatomic gas go through the cycle abc. For the complete cycle, 800 J of heat flows out of the gas. Process ab is at constant pressure, and process bc is at constant volume. States a and b have temperatures Ta = 200 K and Tb = 300 K. (a) Sketch the pV-diagram for the cycle. (b) What is the work W for the process ca?

Three moles of an ideal gas are taken around the cycle \(a c b\) shown in Fig. P19.46. For this gas, \(C_{P}=29.1 \mathrm{~J} / \mathrm{mol} \cdot \mathrm{K}\). Process \(a c\) is at constant pressure, process \(b a\) is at constant volume, and process is adiabatic. The temperatures of the gas in states , , and are \(T_{a}=300\) K, \(T_{c}=492\) K and \(T_{b}=600\) K. Calculate the total work for the cycle. Equation Transcription: Text Transcription: acb C_p=29.1 J/mol.K ac ba cb T_a=300 T_c=492 T_b=600

Figure P19.47 shows a \(p V \text {-diagram }\) for 0.0040 mole of ideal \(\mathrm{H}_{2}\) gas. The temperature of the gas does not change during segment \(b c\). (a) What volume does this gas occupy at point \(c\)? (b) Find the temperature of the gas at points \(a,b\) and \(c\). (c) How much heat went into or out of the gas during segments \(a b, c a\), and \(b c\)? Indicate whether the heat has gone into or out of the gas. (d) Find the change in the internal energy of this hydrogen during segments \(a b, b c\), and \(c a\) Indicate whether the internal energy increased or decreased during each of these segments.

The graph in Fig. P19.48 shows a \(p V \text {-diagram }\) for 3.25 moles of ideal helium \(\text { (He) }\) gas. Part \(c a\) of this process is isothermal. (a) Find the pressure of the He at point (b) Find the temperature of the He at points , and . (c) How much heat entered or left the He during segments \(a b, b c\), and \(c a\)? In each segment, did the heat enter or leave? (d) By how much did the internal energy of the He change from to , from to, and from to ? Indicate whether this energy increased or decreased. Equation Transcription: Text Transcription: pV-diagram (He) ca ab,bc ca p(Pax10^5) V(m^3)

(a) One-third of a mole of \(\text { He }\) gas is taken along the path \(a b c\) shown as the solid line in Fig. Assume that the gas may be treated as ideal. How much heat is transferred into or out of the gas? (b) If the gas instead went from state to state along the horizontal dashed line in Fig. P19.49, how much heat would be transferred into or out of the gas? (c) How does in part (b) compare with in part (a)? Explain. Equation Transcription: Text Transcription: He abc p(Pa) 4x10^5 3x10^5 2x10^5 1x10^5 V(m^3)

Problem 50P Two moles of helium are initially at a temperature of 27.0°C and occupy a volume of 0.0300 m3. The helium first expands at constant pressure until its volume has doubled. Then it expands adiabatically until the temperature returns to its initial value. Assume that the helium can be treated as an ideal gas (a) Draw a diagram of the process in the pV – plane. (b)What is the total heat supplied to the helium in the process? (c) What is the total change in internal energy of the helium? (d) What is the total work done by the helium? (e) What is the final volume of the helium?

Problem 51P Starting with 2.50 mol of N2 gas (assumed to be ideal) in a cylinder at 1.00 atm and 20.0°C, a chemist first heats the gas at volume, adding 1.52 × 104 J of heat, then continues heating and allows the gas to expand at constant pressure to twice its original volume. (a) Calculate the final temperature of the gas. (b). Calculate the amount of work done by the gas. (c) Calculate the amount of heat added to the gas while it was expanding (d) Calculate the change in internal energy of the gas for the whole process.

Problem 52P Nitrogen gas in an expandable container is cooled from 50.0o C to 10.0o C with the pressure held constant at 3.00 X 105 Pa. The total heat liberated by the gas is 2.50 X 104 J. Assume that the gas may be treated as ideal. Find (a) the number of moles of gas; (b) the change in internal energy of the gas; (c) the work done by the gas. (d) How much heat would be liberated by the gas for the same temperature change if the volume were constant?

Problem 53P In a certain process, 2.15 × 105 J of heat is liberated by a system. and at the same time the system contracts under a constant external pressure of 9.50 × 105 Pa. The internal energy of the system is the same at the beginning and end of the process. Find the change in volume of the system. (The system is not an ideal gas.)

CALC A cylinder with a frictionless, movable piston like that shown in Fig. contains a quantity of helium gas. Initially the gas is at a pressure of \(1.00 \times 10^{5}\) Pa, has a temperature of 300 K, and occupies a volume of 1.50 L. The gas then undergoes two processes. In the first, the gas is heated and the piston is allowed to move to keep the temperature equal to 300 K. This continues until the pressure reaches \(2.50 \times 10^{4}\) Pa. In the second process, the gas is compressed at constant pressure until it returns to its original volume of 1.50 L. Assume that the gas may be treated as ideal. (a) In a \(p V \text {-diagram }\), show both processes. (b) Find the volume of the gas at the end of the first process, and find the pressure and temperature at the end of the second process. (c) Find the total work done by the gas during both processes. (d) What would you have to do to the gas to return it to its original pressure and temperature? Equation Transcription: Text Transcription: 1.00x10^5 2.50x10^4 pV-diagram

Problem 55P A Thermodynamic Process in a Liquid. A chemical engineer is studying the properties of liquid methanol (CH3OH). She uses a steel cylinder with a cross-sectional area of 0200 m2 and containing 1.20× 10?2 m3 of methanol. The cylinder is equipped with a tightly fitting piston that supports a loud of 3.00 × 104 N. The temperature of the system is increased from 20.0°C to 50.0°C. For methanol, the coefficient of volume expansion is 1.20 × 10?3 K?1, the density is 791 kg/m3, and the specific heat at constant pressure is cp = 2.51 × 103 J/kg · K. You can ignore the expansion of the steel cylinder. Find (a) the increase in volume of the methanol; (b) the mechanical work done by the methanol against the 3.00 × 104 N force; (c) the amount of heat added to the methanol; (d) the change in internal energy of the methanol. (e) Based on your results, explain whether there is any substantial difference between the specific heats cp (at constant Pressure) and cv (at constant volume) for methanol under these conditions

High-Altitude Research. A large research balloon containing \(2.00 \times 10^{3} \mathrm{~m}^{3}\) of helium gas at 1.00 atm and a temperature of \(15.0^{\circ} \mathrm{C}\) rises rapidly from ground level to an altitude at which the atmospheric pressure is only 0.900 atm (Fig. P19.58). Assume the helium behaves like an ideal gas and the balloon’s ascent is too rapid to permit much heat exchange with the surrounding air. (a) Calculate the volume of the gas at the higher altitude. (b) Calculate the temperature of the gas at the higher altitude. (c) What is the change in internal energy of the helium as the balloon rises to the higher altitude? Equation Transcription: Text Transcription: 2.00x10^3 m^3 15.0degC

Problem 59P Chinook. During certain seasons strong winds called chinooks blow from the west across the eastern slopes of the Rockies and downhill into Denver and nearby areas. Although the mountains are cool, the wind in Denver is very hot; within a few minutes after the chinook wind arrives, the temperature can climb 20 Co (“chinook” refers to a Native American people of the Pacific Northwest). Similar winds occur in the Alps (called foehns) and in southern California (called Santa Anas). (a) Explain why the temperature of the chinook wind rises as it descends the slopes. Why is it important that the wind be fast moving? (b) Suppose a strong wind is blowing toward Denver (elevation 1630 m) from Grays Peak (80 km west of Denver, at an elevation of 4350 m), where the air pressure is 5.60 X 104 Pa and the air temperature is - 15.0o C. The temperature and pressure in Denver before the wind arrives are 2.0o C and 8.12 X 104 Pa. By how many Celsius degrees will the temperature in Denver rise when the chinook arrives?

Problem 60P A certain ideal gas has molar heat capacity at constant volume CV. A sample of this gas initially occupies a volume V0 at pressure p0 and absolute temperature T0. The gas expands isobarically to a volume 2 V0 and then expands further adiabatically to a final volume 4 V0. (a) Draw a pV-diagram for this sequence of processes. (b) Compute the total work done by the gas for this sequence of processes. (c) Find the final temperature of the gas. (d) Find the absolute value of the total heat flow |Q| into or out of the gas for this sequence of processes, and state the direction of heat flow.

Problem 61P An air pump has a cylinder 0.250 m long with a movable piston. The pump is used to compress air from the atmosphere (at absolute pressure 1.01 X 105 Pa) into a very large tank at 3.80 X 105 Pa gauge pressure. (For air, CV = 20.8 J / mol ? K.) (a) The piston begins the compression stroke at the open end of the cylinder. How far down the length of the cylinder has the piston moved when air first begins to flow from the cylinder into the tank? Assume that the compression is adiabatic. (b) If the air is taken into the pump at 27.0o C, what is the temperature of the compressed air? (c) How much work does the pump do in putting 20.0 mol of air into the tank?

Problem 63P A monatomic ideal gas expands slowly to twice its original volume, doing 300 J of work in the process. Find the heat added to the gas and the change in internal energy of the gas if the process is (a) isothermal; (b) adiabatic; (c) isobaric.

Problem 64P CALC A cylinder with a piston contains 0.250 mol of oxygen at 2.40 X 105 Pa and 355 K. The oxygen may be treated as an ideal gas. The gas first expands isobarically to twice its original volume. It is then compressed isothermally back to its original volume, and finally it is cooled isochorically to its original pressure. (a) Show the series of processes on a pV-diagram. Compute (b) the temperature during the isothermal compression; (c) the maximum pressure; (d) the total work done by the piston on the gas during the series of processes.

Problem 65P Use the conditions and processes of Problem 19.54 to compute (a) the work done by the gas, the heat added to it, and its internal energy change during the initial expansion; (b) the work done, the heat added, and the internal energy change during the final cooling; (c) the internal energy change during the isothermal compression. 19.54 .. CALC A cylinder with a piston contains 0.250 mol of oxygen at 2.40 X 105 Pa and 355 K. The oxygen may be treated as an ideal gas. The gas first expands isobarically to twice its original volume. It is then compressed isothermally back to its original volume, and finally it is cooled isochorically to its original pressure. (a) Show the series of processes on a pV-diagram. Compute (b) the temperature during the isothermal compression; (c) the maximum pressure; (d) the total work done by the piston on the gas during the series of processes.

Problem 66P CALC A cylinder with a piston contains 0.150 mol of nitrogen at 1.80 X 105 Pa and 300 K. The nitrogen may be treated as an ideal gas. The gas is first compressed isobarically to half its original volume. It then expands adiabatically back to its original volume, and finally it is heated isochorically to its original pressure. (a) Show the series of processes in a pV-diagram. (b) Compute the temperatures at the beginning and end of the adiabatic expansion. (c) Compute the minimum pressure.

Problem 67P Use the conditions and processes of Problem 19.56 to compute (a) the work done by the gas, the heat added to it, and its internal energy change during the initial compression; (b) the work done by the gas, the heat added to it, and its internal energy change during the adiabatic expansion; (c) the work done, the heat added, and the internal energy change during the final heating. 19.56 .. CALC A cylinder with a piston contains 0.150 mol of nitrogen at 1.80 X 105 Pa and 300 K. The nitrogen may be treated as an ideal gas. The gas is first compressed isobarically to half its original volume. It then expands adiabatically back to its original volume, and finally it is heated isochorically to its original pressure. (a) Show the series of processes in a pV-diagram. (b) Compute the temperatures at the beginning and end of the adiabatic expansion. (c) Compute the minimum pressure.

Problem 68P Comparing Thermodynamic Processes. In a cylinder, 1.20 mol of an ideal monatomic gas, initially at 3.60 X 105 Pa and 300 K, expands until its volume triples. Compute the work done by the gas if the expansion is (a) isothermal; (b) adiabatic; (c) isobaric. (d) Show each process in a pV-diagram. In which case is the absolute value of the work done by the gas greatest? Least? (e) In which case is the absolute value of the heat transfer greatest? Least? (f) In which case is the absolute value of the change in internal energy of the gas greatest? Least?

CP Oscillations of a Piston. A vertical cylinder of radius contains a quantity of ideal gas and is fitted with a piston with mass that is free to move (Fig. ). The piston and the walls of the cylinder are frictionless, and the entire cylinder is placed in a constant-temperature bath. The outside air pressure is \(p_{0}\). In equilibrium, the piston sits at a height above the bottom of the cylinder. (a) Find the absolute pressure of the gas trapped below the piston when in equilibrium. (b) The piston is pulled up by a small distance and released. Find the net force acting on the piston when its base is a distance \(h+y\) above the bottom of the cylinder, where is much less than . (c) After the piston is displaced from equilibrium and released, it oscillates up and down. Find the frequency of these small oscillations. If the displacement is not small, are the oscillations simple harmonic? How can you tell? Equation Transcription: Text Transcription: p_0 h+y p_0

Problem 56P CP A Thermodynamic Process in a Solid. A cube of copper 2.00 cm on a side is suspended by a string. (The physical properties of copper are given in Tables 14.1, 17.2, and 17.3.) The cube is heated with a burner from 20.0o C to 90.0o C. The air surrounding the cube is at atmospheric pressure (1.01 X 105 Pa). Find (a) the increase in volume of the cube; (b) the mechanical work done by the cube to expand against the pressure of the sur-rounding air; (c) the amount of heat added to the cube; (d) the change in internal energy of the cube. (e) Based on your results, explain whether there is any substantial difference between the specific heats cp (at constant pressure) and cV (at constant volume) for copper under these conditions.

BIO A Thermodynamic Process in an Insect. The African bombardier beetle (Stenaptinus insignis) can emit a jet of defensive spray from the movable tip of its abdomen (Fig. P19.57). The beetle’s body has reservoirs of two different chemicals; when the beetle is disturbed, these chemicals are combined in a reaction chamber, producing a compound that is warmed \(20^{\circ} \mathrm{C}\) and \(100^{\circ} \mathrm{C}\) from to by the heat of reaction. The high pressure produced allows the compound to be sprayed out at speeds up to \(19 \mathrm{~m} / \mathrm{s}\) \((68 \mathrm{~km} / \mathrm{h})\), scaring away predators of all kinds. (The beetle shown in the figure is 2 cm long.) Calculate the heat of reaction of the two chemicals (in \(\mathrm{J} / \mathrm{kg}\)). Assume that the specific heat of the two chemicals and the spray is the same as that of water, \(4.19 \times 10^{3} \mathrm{~J} / \mathrm{kg} \cdot \mathrm{K}\), and that the initial temperature of the chemicals is \(20^{\circ} \mathrm{C}\). Equation Transcription: Text Transcription: 20degC 100degC 19 m/s (68 km/h) J/kg 4.19x10^3 J/kg.K 20degC

Problem 62P Engine Turbochargers and Intercoolers. The power output of an automobile engine is directly proportional to the mass of air that can be forced into the volume of the engine’s cylinders to react chemically with gasoline. Many cars have a turbocharger which compresses the air before it enters the engine, giving a greater mass of air per volume. This rapid, essentially adiabatic compression also heats the air. To compress it further, the air then passes through an intercooler in which the air exchanges heat with its surroundings at essentially constant pressure. The air is then drawn into the cylinders. In a typical installation, air is taken into In a typical installation, air is taken into the turbocharger at atmospheric pressure (1.01 × 105 Pa), density ? = 1.23 kg/m3, and temperature 15.0°C. It is compressed adiabatically to 1.45 × 105 Pa. In the intercooler, the air is cooled to the original temperature of 15.0°C at a constant pressure of 1.45 × 105 Pa. (a) Draw a pV-diagram for this sequence of processes. (b) If the volume of one of the engine’s cylinders is 575 cm3, what mass of air exiling from the intercooler will fill the cylinder at 1.45 × 105 Pa? Compared to the power ouput of an engine that takes in air at 1.01 ×105 pa at 15.0°C what percentage increase in power is obtained by using the turbocharger and intercooler? (c) If the intercooier is not used, what mass of air exiting from the turbocharger will fill the cylinder at 1.45 × 105 Pa? Compared to the power output of an engine that takes in air at 1.01 × 105 Pa at 15.0°C, what percentage increase in power is obtained by using the turbocharger alone?