Solution: Boiling Water at High Pressure. When water is

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 gasolineair 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.

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?

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

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.

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?

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

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?

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

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?

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

When you blow on the back of your hand with your mouth wide open, your breath feels warm. But if you partially close your mouth to form an o and then blow on your hand, your breath feels cool. Why?

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 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?

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?

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?

On a sunny day, large bubbles of air form on the sunwarmed 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?

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 condense 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?

Applying the same considerations as in Question Q19.17, explain why the island of Niihau, a few kilometers to the southwest of Kauai, is almost a desert and farms there need to be irrigated.

In a constant-volume process, dU = nCV dT. But in a constant-pressure process, it is not true that dU = nCp dT. Why not?

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?

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?

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 ones temperature would you expect to rise faster? Explain.

A system is taken from state a to state b along the three paths shown in Fig. Q19.23. (a) Along which path is the work done by the system the greatest? The least? (b) If Ub 7 Ua, along which path is the absolute value of the heat transfer, 0 Q 0 , the greatest? For this path, is heat absorbed or liberated by the system? Explain.

A thermodynamic system undergoes a cyclic process as shown in Fig. Q19.24. 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 loop, 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 loop, does heat flow into or out of the system? Explain.

Two moles of an ideal gas are heated at constant pressure from T = 27C to T = 107C. (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 27.0C 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 * 103 J of work

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

A thermodynamic system undergoes a cyclic process as shown in Fig. Q19.24. 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 loop, 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 loop, does heat flow into or out of the system? Explain.

During the time 0.305 mol of an ideal gas undergoes an isothermal compression at 22.0C, 392 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 m3 and the pressure increases from 2.00 * 105 Pa to 5.00 * 105 Pa. The second process is a compression to a volume of 0.120 m3 at a constant pressure of 5.00 * 105 Pa. (a) In a pV-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 0.110 m3 to 0.320 m3 . Heat flows into the gas just rapidly enough to keep the pressure constant at 1.65 * 105 Pa during the expansion. The total heat added is 1.15 * 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?

Five moles of an ideal monatomic gas with an initial temperature of 127C expand and, in the process, absorb 1500 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 mol 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 * 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 * 105 J. (a) Find the work done by the gas. (b) Find the absolute value of the heat flow, 0 Q 0 , 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?

The pV-diagram in Fig. E19.13 shows a process abc involving 0.450 mol of an ideal gas. (a) What was the temperature of this gas at points a, b, and c? (b) How much work was done by or on the gas in this process? (c) How much heat had to be added during the process to increase the internal energy of the gas by 15,000 J?

Boiling Water at High Pressure. When water is boiled at a pressure of 2.00 atm, the heat of vaporization is 2.20 * 106 J>kg and the boiling point is 120C. At this pressure, 1.00 kg of water has a volume of 1.00 * 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.

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? Be specific and explain.

During an isothermal compression of an ideal gas, 410 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 \((\mathrm{CO}_2)\) 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 \(\mathrm{CO}_2\) 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 = 27.0C. (a) How much heat is needed to raise the temperature to 67.0C 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 27.0C to 67.0C? 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 780 K and 3.00 * 106 Pa is contained in a cylinder of volume 40.0 cm3 . 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, repeat part (a).

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 27.0°C and the pressure is constant. As part of a machine design project, calculate the final temperature of the gas after it has done \(2.40 \times 10^{3} \mathrm{\ J}\) of work.

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 \(3.20 \times 10^{-2} \ \mathrm m^3\) to \(4.50 \times 10^{-2} \ \mathrm m^3\) . 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.

An experimenter adds 970 J of heat to 1.75 mol of an ideal gas to heat it from 10.0C to 25.0C 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 g for the gas

Propane gas 1C3H82 behaves like an ideal gas with g = 1.127. Determine the molar heat capacity at constant volume and the molar heat capacity at constant pressure.

The temperature of 0.150 mol of an ideal gas is held constant at 77.0C 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?

Five moles of monatomic ideal gas have initial pressure 2.50 * 103 Pa and initial volume 2.10 m3 . While undergoing an adiabatic expansion, the gas does 1480 J of work. What is the final pressure of the gas after the expansion?

A monatomic ideal gas that is initially at 1.50 * 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?

The engine of a Ferrari F355 F1 sports car takes in air at 20.0C 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 g = 1.40. (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 66.0C to 10.0C. 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?

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 20.0C and 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 1.01 * 105 Pa) is heated by the ground to 26.0C 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 * 105 Pa. Assume that air is an ideal gas, with g = 1.40. (This rate of cooling for dry, rising air, corresponding to roughly 1 C 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 1.00 * 105 Pa and occupies a volume of 2.50 * 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) and pressure of the gas if the expansion is (i) isothermal; (ii) isobaric; (iii) adiabatic.

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. P19.33). (a) In this process, does the temperature of the gas increase, decrease, or stay the same? Explain. (b) If Va = 0.0700 m3 , Vb = 0.1100 m3 , pa = 1.00 * 105 Pa, and pb = 1.40 * 105 Pa, 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. P19.34. (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.

Figure P19.35 shows the pV-diagram for a process in which the temperature of the ideal gas remains constant at \(85^{\circ} \mathrm{C}\). (a) How many moles of gas are involved? (b) What volume does this gas occupy at a? (c) How much work was done by or on the gas from a to b? (d) By how much did the internal energy of the gas change during this process?

The graph in Fig. P19.36 shows a pV-diagram for 3.25 mol 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.

When a system is taken from state a to state b in Fig. P19.37 along 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 Ua = 0 and Ud = 8.0 J, find the heat absorbed in the processes ad and db

A thermodynamic system is taken from state a to state c in Fig. P19.38 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 \(U_a=150\mathrm{\ J},\ U_b=240\mathrm{\ J},\ U_c=680\mathrm{\ J}\text{, }\text{ and }U_d=330\mathrm{\ J}\). 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 path abc in Fig. P19.39. (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 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 1.50 * 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 * 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 * 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?

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 cycle acb shown in Fig. P19.42. For this gas, Cp = 29.1 J>mol # 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 Ta = 300 K, Tc = 492 K, and Tb = 600 K. Calculate the total work W for the cycle.

Figure P19.43 shows a pV-diagram for 0.0040 mol of ideal H2 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 segment.

(a) One-third of a mole of He gas is taken along the path abc shown in Fig. P19.44. 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 directly from state a to state c (a) One-third of a mole of He gas is taken along the path abc shown in Fig. P19.44. 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 directly from state a to state c

Starting with 2.50 mol of \(\mathrm{N}_{2}\) gas (assumed to be ideal) in a cylinder at 1.00 atm and 20.0°C, a chemist first heats the gas at constant volume, adding \(1.36\times 10^4\mathrm{\ J}\) of heat, then continues heating and allows the gas to expand at constant pressure to twice its original volume. Calculate (a) the final temperature of the gas; (b) the amount of work done by the gas; (c) the amount of heat added to the gas while it was expanding; (d) the change in internal energy of the gas for the whole process.

Nitrogen gas in an expandable container is cooled from 50.0C to 10.0C with the pressure held constant at 3.00 * 105 Pa. The total heat liberated by the gas is 2.50 * 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?

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 \(1.00\times 10^5\mathrm{\ Pa}\) and 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 at 300 K. This continues until the pressure reaches \(2.50\times 10^4\mathrm{\ Pa}\). 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 pV-diagram, show both processes. (b) Find the volume of the gas at the end of the first process, and 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 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 20.0C to 90.0C. The air surrounding the cube is at atmospheric pressure 11.01 * 105 Pa2. 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 cp (at constant pressure) and cV (at constant volume) for copper under these conditions.

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 C (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 * 104 Pa and the air temperature is -15.0C. The temperature and pressure in Denver before the wind arrives are 2.0C and 8.12 * 104 Pa. By how many Celsius degrees will the temperature in Denver rise when the chinook arrives?

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. P19.50). 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?

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 * 105 Pa) into a very large tank at 3.80 * 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 27.0C, 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?

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 2V0 and then expands further adiabatically to a final volume 4V0. (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 0 Q 0 into or out of the gas for this sequence of processes, and state the direction of heat flow.

A monatomic ideal gas expands slowly to twice its original volume, doing 450 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.

A cylinder with a piston contains 0.250 mol of oxygen at 2.40 * 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.

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.

A cylinder with a piston contains 0.150 mol of nitrogen at 1.80 * 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.

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

Comparing Thermodynamic Processes. In a cylinder, 1.20 mol of an ideal monatomic gas, initially at \(3.60\times 10^5\mathrm{\ Pa}\) 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?

You have recorded measurements of the heat flow Q into 0.300 mol of a gas that starts at \(T_1 = 20.0^\circ \mathrm C\) and ends at a temperature \(T_2\). You measured Q for three processes: one isobaric, one isochoric, and one adiabatic. In each case, \(T_2\) was the same. Figure P19.59 summarizes your results. But you lost a page from your lab notebook and don’t have a record of the value of \(T_2\); you also don’t know which process was isobaric, isochoric, or adiabatic. Each process was done at a sufficiently low pressure for the gas to be treated as ideal. (a) Identify each process a, b, or c as isobaric, isochoric, or adiabatic. (b) What is the value of \(T_2\)? (c) How much work is done by the gas in each process? (d) For which process is the magnitude of the volume change the greatest? (e) For each process, does the volume of the gas increase, decrease, or stay the same?

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

You place a quantity of gas into a metal cylinder that has a movable piston at one end. No gas leaks out of the cylinder as the piston moves. The external force applied to the piston can be varied to change the gas pressure as you move the piston to change the volume of the gas. A pressure gauge attached to the interior wall of the cylinder measures the gas pressure, and you can calculate the volume of the gas from a measurement of the pistons position in the cylinder. You start with a pressure of 1.0 atm and a gas volume of 3.0 L. Holding the pressure constant, you increase the volume to 5.0 L. Then, keeping the volume constant at 5.0 L, you increase the pressure to 3.0 atm. Next you decrease the pressure linearly as a function of volume until the volume is 3.0 L and the pressure is 2.0 atm. Finally, you keep the volume constant at 3.0 L and decrease the pressure to 1.0 atm, returning the gas to its initial pressure and volume. The walls of the cylinder are good conductors of heat, and you provide the required heat sources and heat sinks so that the necessary heat flows can occur. At these relatively high pressures, you suspect that the ideal-gas equation will not apply with much accuracy. You dont know what gas is in the cylinder or whether it is monatomic, diatomic, or polyatomic. (a) Plot the cycle in the pV@plane. (b) What is the net heat flow for the gas during this cycle? Is there net heat flow into or out of the gas?

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 \(\left(1.01 \times 10^5 \mathrm{~Pa}\right)\), density \(\rho=1.23 \mathrm{~kg} / \mathrm{m}^3\), and temperature \(15.0^{\circ} \mathrm{C}\). It is compressed adiabatically to \(1.45 \times 10^5 \mathrm{~Pa}\). In the intercooler, the air is cooled to the original temperature of \(15.0^{\circ} \mathrm{C}\) at a constant pressure of \(1.45 \times 10^5 \mathrm{~Pa}\). (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 \(1.45 \times 10^5 \mathrm{~Pa}\) ? Compared to the power output of an engine that takes in air at \(1.01 \times 10^5 \mathrm{~Pa}\) 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 \(1.45 \times 10^5 \ \mathrm{Pa}\)? Compared to the power output of an engine that takes in air at \(1.01 \times 10^5\ \mathrm{Pa}\) at \(15.0^\circ\mathrm{C}\), what percentage increase in power is obtained by using the turbocharger alone?

In a test of the effects of low temperatures on the gas mixture, a cylinder filled at 20.0C to 2000 psi (gauge pressure) is cooled slowly and the pressure is monitored. What is the expected pressure at -5.00C if the gas remains a homogeneous mixture? (a) 500 psi; (b) 1500 psi; (c) 1830 psi; (d) 1920 psi.

In another test, the valve of a 500-L cylinder full of the gas mixture at 2000 psi (gauge pressure) is opened wide so that the gas rushes out of the cylinder very rapidly. Why might some \(\mathrm{N}_{2} \mathrm{O}\) condense during this process? (a) This is an isochoric process in which the pressure decreases, so the temperature also decreases. (b) Because of the rapid expansion, heat is removed from the system, so the internal energy and temperature of the gas decrease. (c) This is an isobaric process, so as the volume increases, the temperature decreases proportionally. (d) With the rapid expansion, the expanding gas does work with no heat input, so the internal energy and temperature of the gas decrease.

You have a cylinder that contains 500 L of the gas mixture pressurized to 2000 psi (gauge pressure). A regulator sets the gas flow to deliver 8.2 L/min at atmospheric pressure. Assume that this flow is slow enough that the expansion is isothermal and the gases remain mixed. How much time will it take to empty the cylinder? (a) 1 h; (b) 33 h; (c) 57 h; (d) 140 h.

In a hospital, pure oxygen may be delivered at 50 psi (gauge pressure) and then mixed with \(\mathrm N_2 \mathrm O\). What volume of oxygen at \(20^\circ \mathrm C\) and 50 psi (gauge pressure) should be mixed with 1.7 kg of \(\mathrm N_2 \mathrm O\) to get a 50%/50% mixture by volume at \(20^\circ \mathrm C\)? (a) \(0.21 \ \mathrm {m}^3\) ; (b) \(0.27 \ \mathrm {m}^3\) ; (c) \(1.9 \ \mathrm {m}^3\) ; (d) \(100 \ \mathrm {m}^3\).