Solved: Section 17.7 The Specific Heats of GasesA gas

In Problems 74 through 76 you are given the equation used to solve a problem. For each of these, you are to a. Write a realistic problem for which this is the correct equation. b. Finish the solution of the problem. \((10 \mathrm{~atm}) V_{2}^{1.40}=(1.0 \mathrm{~atm}) V_{1}^{1.40}\) Equation Transcription: Text Transcription: (10 atm)V_2^1.40=(1.0 atm)V_1^1.40

In Problems 74 through 76 you are given the equation used to solve a problem. For each of these, you are to a. Write a realistic problem for which this is the correct equation. b. Finish the solution of the problem. \(\left(200 \times 10^{-6} \mathrm{~m}^{3}\right)\left(13,600 \mathrm{~kg} / \mathrm{m}^{3}\right)\) \(\times(140 \mathrm{~J} / \mathrm{kgK})\left(90^{\circ} \mathrm{C}-15^{\circ} \mathrm{C}\right)+(0.50 \mathrm{~kg})(449 \mathrm{~J} / \mathrm{kg} K)\left(90^{\circ} \mathrm{C}-T_{i}\right)=0\) Equation Transcription: Text Transcription: (200x10^-6m3)(13,600 kg/m^3) x(140J/kg K)90^circ C-15^circC)+(0.50 kg)(449J/kg K)(90^circC-T_i)=0

In Problems 74 through 76 you are given the equation used to solve a problem. For each of these, you are to a. Write a realistic problem for which this is the correct equation. b. Finish the solution of the problem. \(50 \mathrm{~J}=-n(8.31 \mathrm{~J} / \mathrm{molK})(350 \mathrm{~K}) \ln \left(\frac{1}{3}\right)\) Equation Transcription: Text Transcription: 50J=-n(8.31 J/molK)(350 K)ln (1/3 )

Problem 73P The sun’s intensity at the distance of the earth is 1370 W/m2. 30% of this energy is reflected by water and clouds; 70% is absorbed. What would be the earth’s average temperature (in °C) if the earth had no atmosphere? The emissivity of the surface is very close to 1. (The actual average temperature of the earth, about 15°C, is higher than your calculation because of the greenhouse effect.)

Problem 78CP One cylinder in the diesel engine of a truck has an initial volume of 600 cm3. Air is admitted to the cylinder at 30°C and a pressure of 1.0 atm. The piston rod then does 400 J of work to rapidly compress the air. What are its final temperature and volume?

Figure CP17.77 shows a thermodynamic process followed by \(120 \mathrm{mg}\) of helium. a. Determine the pressure (in atm), temperature (in \(\left.{ }^{\circ} \mathrm{C}\right)\), and volume (in \(\mathrm{cm}^{3}\) ) of the gas at points 1,2 , and 3 . Put your results in a table for easy reading. Equation Transcription: Text Transcription: 120 mg ^circC cm^3

Problem 79CP You come into lab one day and find a well-insulated 2000 mL thermos bottle containing 500 mL of boiling liquid nitrogen. The remainder of the thermos has nitrogen gas at a pressure of 1.0 atm. The gas and liquid are in thermal equilibrium. While waiting for lab to start, you notice a piece of iron on the table with “197 g” written on it. Just for fun, you drop the iron into the thermos and seal the cap tightly so that no gas can escape. After a few seconds have passed, what is the pressure inside the thermos? The density of liquid nitrogen is 810 kg/m3.

Problem 80CP A cylindrical copper rod and an iron rod with exactly the same dimensions are welded together end to end. The outside end of the copper rod is held at 100°C, and the outside end of the iron rod is held at 0°C. What is the temperature at the midpoint where the rods are joined together?

Problem 1CQ When the space shuttle returns to earth, its surfaces get very hot as it passes through the atmosphere at high speed. Has the space shuttle been heated? If so, what was the source of the heat? If not, why is it hot?

Problem 81CP 0.020 mol of a diatomic gas, with initial temperature 20°C, are compressed from 1500 cm3 to 500 cm3 in a process in which pV 2 = constant. How much heat is added during this process?

A monatomic gas fills the left end of the cylinder in Figure CP17.82. At \(300 \mathrm{~K}\), the gas cylinder length is \(10.0 \mathrm{~cm}\) and the spring is compressed by \(2.0 \mathrm{~cm}\). How much heat energy must be added to the gas to expand the cylinder length to \(16.0 \mathrm{~cm}\) ? Equation Transcription: Text Transcription: 300 K 10.0 cm 2.0 cm 16.0 cm

Problem 2CQ Do (a) temperature, (b) heat, and (c) thermal energy describe a property of a system, an interaction of the system with its environment, or both? Explain.

How much work is done on the gas in the process shown in Figure EX17.1? Figure EX17.1

Two containers hold equal masses of nitrogen gas at equal temperatures. You supply \(10 \mathrm{~J}\) of heat to container \(A\) while not allowing its volume to change, and you supply \(10 \mathrm{~J}\) of heat to container \(B\) while not allowing its pressure to change. Afterward, is temperature \(T_{A}\) greater than, less than, or equal to \(T_{B}\)? Explain. Equation Transcription: Text Transcription: 10 J 10 J A B T_A T_B

How much work is done on the gas in the process shown in Figure EX17.2? Figure EX17.2

\(80 \mathrm{~J} \text { of work are done on the gas in the process shown in Figure EX17.3. What is } V_{1} \text { in } \mathrm{cm}^{3} \text { ? }\) Equation Transcription: Text Transcription: 80 J V_1 cm^3

Problem 4CQ You need to raise the temperature of a gas by 10°C. To use the smallest amount of heat energy, should you heat the gas at constant pressure or at constant volume? Explain.

Problem 5CQ Why is the molar specific heat of a gas at constant pressure larger than the molar specific heat at constant volume?

Problem 4E Section 17.1 It ’s All About Energy Section 17.2 Work in Ideal-Gas Processes A 2000 cm3 container holds 0.10 mol of helium gas at 300°C. How much work must be done to compress the gas to 1000 cm3 at (a) constant pressure and (b) constant temperature?

Draw a first-law bar chart (see Figure 17.14) for the gas process in Figure EX17.5. Figure EX17.5

Figure Q17.6 shows an adiabatic process. a. Is the final temperature higher than, lower than, or equal to the initial temperature? b. Is any heat energy added to or removed from the system in this process? Explain. Figure Q17.6

Draw a first-law bar chart (see Figure 17.14) for the gas process in Figure EX17.6. Figure EX17.6

Draw a first-law bar chart (see Figure 17.14) for the gas process in Figure EX17.7. Figure EX17.7

Figure Q17.8 shows two different processes taking an ideal gas from state i to state \(f\). a. Is the temperature change \(\Delta T\) during process A larger than, smaller than, or equal to the change during process B? Explain. b. Is the heat energy added during process A greater than, less than, or equal to the heat added during process B? Explain. Equation Transcription: Text Transcription: f Delta T

Figure Q17.7 shows two different processes taking an ideal gas from state i to state \(f\). Is the work done on the gas in process A greater than, less than, or equal to the work done in process B? Explain. Equation Transcription: Text Transcription: f

Problem 9E Section 17.3 Heat Section 17.4 The First Law of Thermodynamics A gas is compressed from 600 cm3 to 200 cm3 at a constant pressure of 400 kPa. At the same time, 100 J of heat energy is transferred out of the gas. What is the change in thermal energy of the gas during this process?

Describe a series of steps in which you use the cylinder of Figure 17.13 to implement the ideal-gas process shown in FIGURE Q17.9. Then show the process as a first-law bar chart. FIGURE Q17.9

Draw a first-law bar chart (see Figure 17.14) for the gas process in FIGURE EX17.8. FIGURE EX17.8

Describe a series of steps in which you use the cylinder of Figure to implement the ideal-gas process shown in FIGURE Q17.10. Then show the process as a first-law bar chart. FIGURE Q17.10

Problem 10E 500 J of work are done on a system in a process that decreases the system’s thermal energy by 200 J. How much energy is transferred to or from the system as heat?

The gas cylinder in FIGURE Q17.11, similar to the cylinder shown in Figure 17.13, is placed on a block of ice. The initial gas temperature is \(>0^{\circ} \mathrm{C}\). a. During the process that occurs until the gas reaches a new equilibrium, are (i) \(\Delta T\), (ii) \(W\), and (iii) \(Q\) greater than, less than, or equal to zero? Explain. b. Draw a \(p V\) diagram showing the process. Equation Transcription: Text Transcription: >0 ^circC Delta T, W, Q pV

Problem 11E Section 17.5 Thermal Properties of Matter How much heat energy must be added to a 6.0 cm × 6.0 cm × 6.0 cm block of aluminum to raise its temperature from ?50°C to 50°C?

Problem 13E Section 17.5 Thermal Properties of Matter a. 100 J of heat energy are transferred to 20 g of mercury. By how much does the temperature increase? ________________ b. How much heat is needed to raise the temperature of 20 g of water by the same amount?

Problem 15E Section 17.5 Thermal Properties of Matter What is the maximum mass of ethyl alcohol you could boil with 1000 J of heat, starting from 20°C?

Problem 12E Section 17.5 Thermal Properties of Matter A rapidly spinning paddle wheel raises the temperature of 200 mL of water from 21°C to 25°C. How much (a) heat is transferred and (b) work is done in this process?

Problem 14E Section 17.5 Thermal Properties of Matter How much heat is needed to change 20 g of mercury at 20°C into mercury vapor at the boiling point?

The gas cylinder in FIGURE Q17.12 is similar to the cylinder described earlier in Figure 17.13, except that the bottom is insulated. Masses are slowly removed from the top of the piston until the total mass is reduced by \(50 \%\). a. During this process, are (i) \(\Delta T\), (ii) \(W\), and (iii) \(Q\) greater than, less than, or equal to zero? Explain. b. Draw a \(p V\) diagram showing the process. Equation Transcription: Text Transcription: 50% Delta T,W,Q pV

Problem 16E 30 g of copper pellets are removed from a 300°C oven and immediately dropped into 100 mL of water at 20°C in an insulated cup. What will the new water temperature be?

Problem 17E Section 17.6 Calorimetry A 750 g aluminum pan is removed from the stove and plunged into a sink filled with 10.0 L of water at 20.0°C. The water temperature quickly rises to 24.0°C. What was the initial temperature of the pan in °C and in °F?

Problem 18E Section 17.6 Calorimetry A 50.0 g thermometer is used to measure the temperature of 200 mL of water. The specific heat of the thermometer, which is mostly glass, is 750 J/kg K, and it reads 20.0°C while lying on the table. After being completely immersed in the water, the thermometer’s reading stabilizes at 71.2°C. What was the actual water temperature before it was measured?

Problem 21E A container holds 1.0 g of argon at a pressure of 8.0 atm. a. How much heat is required to increase the temperature by 100°C at constant volume? b. How much will the temperature increase if this amount of heat energy is transferred to the gas at constant pressure?

Problem 19E A 500 g metal sphere is heated to 300°C, then dropped into a beaker containing 4.08 kg of mercury at 20.0°C. A short time later the mercury temperature stabilizes at 99.0°C. Identify the metal.

Problem 22E A container holds 1.0 g of oxygen at a pressure of 8.0 atm. a. How much heat is required to increase the temperature by 100°C at constant pressure? b. How much will the temperature increase if this amount of heat energy is transferred to the gas at constant volume?

Problem 20E Section 17.6 Calorimetry A 65 cm3 block of iron is removed from an 800°C furnace and immediately dropped into 200 mL of 20°C water. What fraction of the water boils away?

Problem 23E Section 17.7 The Specific Heats of Gases A rigid cylinder contains 7.0 g of nitrogen at 20°C. What is the minimum amount of heat energy that must be removed to liquify the nitrogen?

Problem 24E Section 17.7 The Specific Heats of Gases The volume of a gas is halved during an adiabatic compression that increases the pressure by a factor of 2.5. a. What is the specific heat ratio ? ? ________________ b. By what factor does the temperature increase?

Problem 25E Section 17.7 The Specific Heats of Gases A gas cylinder holds 0.10 mol of O2 at 150°C and a pressure of 3.0 atm. The gas expands adiabatically until the pressure is halved. What are the final (a) volume and (b) temperature?

Problem 28E Section 17.8 Heat-Transfer Mechanisms The ends of a 20-cm-long, 2.0-cm-diameter rod are maintained at 0°C and 100°C by immersion in an ice-water bath and boiling water. Heat is conducted through the rod at 4.5 × 104 J per hour. Of what material is the rod made?

Problem 29E Section 17.8 Heat-Transfer Mechanisms What maximum power can be radiated by a 10-cm-diameter solid lead sphere? Assume an emissivity of 1.

Problem 27E Section 17.8 Heat-Transfer Mechanisms A 10 m × 14 m house is built on a 12-cm-thick concrete slab. What is the heat-loss rate through the slab if the ground temperature is 5°C while the interior of the house is 22°C?

Problem 30E Section 17.8 Heat-Transfer Mechanisms Radiation from the head is a major source of heat loss from the human body. Model a head as a 20-cm-diameter, 20-cm-tall cylinder with a flat top. If the body’s surface temperature is 35°C, what is the net rate of heat loss on a chilly 5°C day? All skin, regardless of color, is effectively black in the infrared where the radiation occurs, so use an emissivity of 0.95.

Problem 26E Section 17.7 The Specific Heats of Gases A gas cylinder holds 0.10 mol of O2 at 150°C and a pressure of 3.0 atm. The gas expands adiabatically until the volume is doubled. What are the final (a) pressure and (b) temperature?

Problem 31P A 5.0 g ice cube at ?20°C is in a rigid, sealed container from which all the air has been evacuated. How much heat is required to change this ice cube into steam at 200°C?

Problem 33P An 11 kg bowling ball at 0°C is dropped into a tub containing a mixture of ice and water. A short time later, when a new equilibrium has been established, there are 5.0 g less ice. From what height was the ball dropped? Assume no water or ice splashes out.

Problem 32P A 5.0-m-diameter garden pond is 30 cm deep. Solar energy is incident on the pond at an average rate of 400 W/m2. If the water absorbs all the solar energy and does not exchange energy with its surroundings, how many hours will it take to warm from 15°C to 25°C?

Problem 34P The burner on an electric stove has a power output of 2.0 kW. A 750 g stainless steel teakettle is filled with 20°C water and placed on the already hot burner. If it takes 3.0 min for the water to reach a boil, what volume of water, in cm3, was in the kettle? Stainless steel is mostly iron, so you can assume its specific heat is that of iron.

Problem 36P One way you keep from overheating is by perspiring. Evaporation—a phase change—requires heat, and the heat energy is removed from your body. Evaporation is much like boiling, only water’s heat of vaporization at 35°C is a somewhat larger 24 × 105 J/kg because at lower temperatures more energy is required to break the molecular bonds. Very strenuous activity can cause an adult human to produce 30 g of perspiration per minute. If all the perspiration evaporates, rather than dripping off, at what rate (in J/s) is it possible to exhaust heat by perspiring?

Problem 37P When air is inhaled, it quickly becomes saturated with water vapor as it passes through the moist airways. Consequently, an adult human exhales about 25 mg of evaporated water with each breath. Evaporation—a phase change—requires heat, and the heat energy is removed from your body. Evaporation is much like boiling, only water’s heat of vaporization at 35°C is a somewhat larger 24 × 105 J/kg because at lower temperatures more energy is required to break the molecular bonds. At 12 breaths/min, on a dry day when the inhaled air has almost no water content, what is the body’s rate of energy loss (in J/s) due to exhaled water? (For comparison, the energy loss from radiation, usually the largest loss on a cool day, is about 100 J/s.)

Problem 38P Two cars collide head-on while each is traveling at 80 km/h. Suppose all their kinetic energy is transformed into the thermal energy of the wrecks. What is the temperature increase of each car? You can assume that each car’s specific heat is that of iron.

Problem 35P Reptiles don’t use enough metabolic energy to keep their body temperature constant. They cool off at night and must warm up in the morning sun. Suppose a 2.9-m-long, 60-cm-wide, 350 kg alligator is basking in the sun. If the sun’s intensity on the back of the alligator is 500 W/m2, and if energy losses can be ignored, how long will it take the alligator to warm up from 23°C to a more favorable 30°C? The average specific heat of body tissue is 3400 J/kg K.

Problem 39P 10 g of aluminum at 200°C and 20 g of copper are dropped into 50 cm3 of ethyl alcohol at 15°C. The temperature quickly comes to 25°C. What was the initial temperature of the copper?

Problem 40P A 100 g ice cube at ?10°C is placed in an aluminum bucket whose initial temperature is 70°C. The system comes to an equilibrium temperature of 20°C. What is the mass of the bucket?

Problem 41P 512 g of an unknown metal at a temperature of 15°C is dropped into a 100 g aluminum container holding 325 g of water at 98°C. A short time later, the container of water and metal stabilizes at a new temperature of 78°C. Identify the metal.

Problem 43P What is oxygen’s specific heat at constant volume in J/kgK?

Problem 42P A 150 L ( ? 40gal) electric hot-water tank has a 5.0 kW heater. How many minutes will it take to raise the water temperature from 65°F to 140°F?

An experiment measures the temperature of a \(500 \mathrm{~g}\) substance while steadily supplying heat to it. Figure P17.45 shows the results of the experiment. What are the (a) specific heat of the solid phase, (b) specific heat of the liquid phase, (c) melting and boiling temperatures, and (d) heats of fusion and vaporization? Equation Transcription: Text Transcription: 500 g

Problem 44P Suppose you take and hold a deep breath on a chilly day, inhaling 3.0 L of air at 0°C and 1 atm. a. How much heat must your body supply to warm the air to your internal body temperature of 37°C? ________________ b. By how much does the air’s volume increase as it warms?

Problem 46P Your 300 mL cup of coffee is too hot to drink when served at 90°C. What is the mass of an ice cube, taken from a ?20°C freezer, that will cool your coffee to a pleasant 60°C?

A beaker with a metal bottom is filled with \(20 \mathrm{~g}\) of water at \(20^{\circ} \mathrm{C}\). It is brought into good thermal contact with a \(4000 \mathrm{~cm}^{3}\) container holding \(0.40 \mathrm{~mol}\) of a monatomic gas at \(10 \mathrm{~atm}\) pressure. Both containers are well insulated from their surroundings. What is the gas pressure after a long time has elapsed? You can assume that the containers themselves are nearly massless and do not affect the outcome. Equation Transcription: Text Transcription: 20 g 20^circC 4000 cm^3 0.40 mol 10 atm

Problem 49P 2.0 mol of gas are at 30°C and a pressure of 1.5 atm. How much work must be done on the gas to compress it to one third of its initial volume at (a) constant temperature and (b) constant pressure? (c) Show both processes on a single pV diagram.

Problem 50P 500 J of work must be done to compress a gas to half its initial volume at constant temperature. How much work must be done to compress the gas by a factor of 10, starting from its initial volume?

Problem 47P A typical nuclear reactor generates 1000 MW (1000 MJ/s) of electrical energy. In doing so, it produces 2000 MW of “waste heat” that must be removed from the reactor to keep it from melting down. Many reactors are sited next to large bodies of water so that they can use the water for cooling. Consider a reactor where the intake water is at 18°C. State regulations limit the temperature of the output water to 30°C so as not to harm aquatic organisms. How many liters of cooling water have to be pumped through the reactor each minute?

A \(6.0\)-cm-diameter cylinder of nitrogen gas has a \(4.0\)-cm-thick movable copper piston. The cylinder is oriented vertically, as shown in Figure P17.51, and the air above the piston is evacuated. When the gas temperature is \(20^{\circ} \mathrm{C}\), the piston floats \(20 \mathrm{~cm}\) above the bottom of the cylinder. a. What is the gas pressure? b. How many gas molecules are in the cylinder? Then \(2.0 \mathrm{~J}\) of heat energy are transferred to the gas. c. What is the new equilibrium temperature of the gas? d. What is the final height of the piston? e. How much work is done on the gas as the piston rises? Equation Transcription: Text Transcription: 6.0 cm 4.0 cm 20 ^circ C 20 cm 2.0 J

Problem 52P A 10-cm-diameter cylinder contains argon gas at 10 atm pressure and a temperature of 50°C. A piston can slide in and out of me cyunder. The cylinder’s initial length is 20 cm. 2500 J of heat are transferred to the gas, causing the gas to expand at constant pressure. What are (a) the final temperature and (b) the final length of the cylinder?

Problem 53P A cube 20 cm on each side contains 3.0 g of helium at 20°C. 1000 J of heat energy are transferred to this gas. What are (a) the final pressure if the process is at constant volume and (b) the final volume if the process is at constant pressure? (c) Show and label both processes on a single pV diagram.

Problem 54P An 8.0-cm-diameter, well-insulated vertical cylinder containing nitrogen gas is sealed at the top by a 5.1 kg frictionless piston. The air pressure above the piston is 100 kPa. a. What is the gas pressure inside the cylinder? ________________ b. Initially, the piston height above the bottom of the cylinder is 26 cm. What will be the piston height if an additional 3.5 kg are placed on top of the piston?

\(0.10 \mathrm{~mol}\) of nitrogen gas follow the two processes shown in Figure P17.58. How much heat is required for each? Equation Transcription: Text Transcription: 0.10 mol

Figure P17.57 shows two processes that take a gas from state \(i\) to state \(f\). Show that \(Q_{A}-Q_{B}=p_{i} V_{i}\). Equation Transcription: Text Transcription: i f Q_A-Q_B=p_iV_i

\(0.10 \mathrm{~mol}\) of nitrogen gas follow the two processes shown in Figure P17.59. How much heat is required for each? Equation Transcription: Text Transcription: 0.10 mol

Problem 55P n moles of an ideal gas at temperature T 1 and volume V 1 expand isothermally until the volume has doubled. In terms of n, T 1 and V 1, what are (a) the final temperature, (b) the work done on the gas, and (c) the heat energy transferred to the gas?

\(0.10 \mathrm{~mol}\) of a monatomic gas follow the process shown in Figure P17.60. a. How much heat energy is transferred to or from the gas during process \(1 \rightarrow 2\)? b. How much heat energy is transferred to or from the gas during process \(2 \rightarrow 3\) ? c. What is the total change in thermal energy of the gas? Equation Transcription: Text Transcription: 0.10 mol 1 rightarrow 2 2 rightarrow 3

Problem 62P Two cylinders each contain 0.10 mol of a diatomic gas at 300 K and a pressure of 3.0 atm. Cylinder A expands isother-mally and cylinder B expands adiabatically until the pressure of each is 1.0 atm. a. What are the final temperature and volume of each? ________________ b. Show both processes on a single pV diagram. Use an appropriate scale on both axes.

Problem 61P Your laboratory assignment for the week is to measure the specific heat ratio ? of carbon dioxide. The gas is contained in a cylinder with a movable piston and a thermometer. When the piston is withdrawn as far as possible, the cylinder’s length is 20 cm. You decide to push the piston in very rapidly by various amounts and, for each push, to measure the temperature of the carbon dioxide. Before each push, you withdraw the piston all the way and wait several minutes for the gas to come to the room temperature of 21°C. Your data are as follows: Push (cm) Temperature ( °C) 5 35 10 68 13 110 15 150 Use the best-fit line of an appropriate graph to determine ? for carbon dioxide.

Figure P17.64 shows a thermodynamic process followed by \(0.015 \mathrm{~mol}\) of hydrogen. How much heat energy is transferred to the gas? Equation Transcription: Text Transcription: 0.015 mol

Figure P17.65 shows a thermodynamic process followed by \(120 \mathrm{mg}\)of helium. a. Determine the pressure (in atm), temperature (in \(\left.{ }^{\circ} \mathrm{C}\right)\), and volume (in \(\mathrm{cm}^{3}\) ) of the gas at points 1,2 , and 3 . Put your results in a table for easy reading. b. How much work is done on the gas during each of the three segments? c. How much heat energy is transferred to or from the gas during each of the three segments? Equation Transcription: Text Transcription: 120 mg ^circC cm63

A monatomic gas follows the process \(1 \rightarrow 2 \rightarrow 3\) shown in Figure P17.63. How much heat is needed for (a) process \(1 \rightarrow 2\) and (b) process \(2 \rightarrow 3\)? Equation Transcription: Text Transcription: 1 rightarrow 2 rightarrow 3 1 rightarrow 2 2 rightarrow 3

Problem 67P Two containers of a diatomic gas have the same initial conditions. One container, heated at constant pressure, has a temperature increase of 20°C. The other container receives the same quantity of heat energy, but at constant volume. What is its temperature increase?

Problem 66P a. What compression ratio V max /V min will raise the air temperature from 20°C to 1000°C in an adiabalic process? ________________ b. What pressure ratio p max /p min does this process have?

Problem 69P 14 g of nitrogen gas at STP are pressurized in an isochoric process to a pressure of 20 atm. What are (a) the final temperature, (b) the work done on the gas, (c) the heat input to the gas, and (d) the pressure ratio p max /p min ? (e) Show the process on a pV diagram, using proper scales on both axes.

Problem 72P A cubical box 20 cm on a side is constructed from 1.2-cm-thick concrete panels. A 100 W lightbtilb is sealed inside the box. What is the air temperature inside the box when the light is on if the surrounding air temperature is 20°C?

Problem 71P You would like to put a solar hot water system on your roof, but you’re not sure it’s feasible. A reference book on solar energy shows that the ground-level solar intensity in your city is 800 W/m2 for at least 5 hours a day throughout most of the year. Assuming that a completely black collector plate loses energy only by radiation, and that the air temperature is 20°C, what is the equilibrium temperature of a collector plate directly facing the sun? Note that while a plate has two sides, only the side facing the sun will radiate because the opposite side will be well insulated.

Problem 68P 14 g of nitrogen gas at STP are adiabatically compressed to a pressure of 20 atm. What are (a) the final temperature, (b) the work done on the gas, (c) the heat input to the gas, and (d) the compression ratio V max /V min ? (e) Show the process on a pV diagram, using proper scales on both axes.

Problem 70P When strong winds rapidly carry air down from mountains to a lower elevation, the air has no time to exchange heat with its surroundings. The air is compressed as the pressure rises, and its temperature can increase dramatically. These warm winds are called Chinook winds in the Rocky Mountains and Santa Ana winds in California. Suppose the air temperature high in the mountains behind Los Angeles is 0°C at an elevation where the air pressure is 60 kPa. What will the air temperature be, in °C and °F, when the Santa Ana winds have carried this air down to an elevation near sea level where the air pressure is 100 kPa?

Problem 56P 5.0 g of nitrogen gas at 20°C and an initial pressure of 3.0 atm undergo an isobaric expansion until the volume has tripled. a. What are the gas volume and temperature after the expansion? ________________ b. How much heat energy is transferred to the gas to cause mis expansion? The gas pressure is then decreased at constant volume until the original temperature is reached. c. What is the gas pressure after the decrease? ________________ d. What amount of heat energy is transferred from the gas as its pressure decreases? ________________ e. Show the total process on a pV diagram. Provide an appropriate scale on both axes.