Questions and Answers of Fundamentals Of Thermodynamics

Carbon dioxide is used in an ideal gas refrigeration cycle, the reverse of Fig. 5.24. Heat absorption is at 250 K and heat rejection is at 325 K where the pressure changes from 1200 kPa to 2400 kPa.
The ocean near Hawaii is 20°C near the surface and 5°C at some depth. A power plant based on this temperature difference is being planned. How large an efficiency could it have? If the two heat
A large heat pump should upgrade 5 MW of heat at 85°C to be delivered as heat at 150°C. Suppose the actual heat pump has a COP of 2.5. How much power is required to drive the unit? For the same
A car engine with a thermal efficiency of 33% drives the air-conditioner unit (a refrigerator) as well as powering the car and other auxiliary equipment. On a hot (35◦C) summer day the air
In a remote location, you run a heat engine to provide the power to run a refrigerator. The input to the heat engine is 800 K and the low T is 400 K; it has an actual efficiency equal to half of that
A refrigerator maintaining a 5°C inside temperature is located in a 30°C room. It must have a high temperature ΔT above room temperature and a low temperature ΔT below the refrigerated space in
A nuclear reactor provides a flow of liquid sodium at 800°C, which is used as the energy source in a steam power plant. The condenser cooling water comes from a nearby river at 15°C. Determine the
Consider the setup with two stacked (temperature wise) heat engines, as in Fig. P5.4. Let TH =850 K, TM = 600 K, and TL = 350 K. Find the two heat engine efficiencies and the combined overall
Calculate the COP of the R-134a refrigerator described in Example 4.8.Example 4.8.The refrigerator shown in Fig. 4.12 uses R-134a as the working fluid. The mass flow rate through each component is
In Example 2.1b, is there any mass at the indicated specific volume? Explain.
A portable fan blows 0.3 kg/s room air with a velocity of 15 m/s (see Fig. P4.18). What is the minimum power electric motor that can drive it? FIGURE P4.18
R-410a at−5◦C, 700 kPa is throttled, so it becomes cold at −40◦C. What is exit P?
For one of the substances in Table A.6, compare the enthalpy change between any two temperatures, T1 and T2, as calculated by integrating the specific heat equation; by assuming constant specific
Reconsider the process in Problem 3.170, in which three states were specified. Solve the problem by fitting a single smooth curve (P versus v) through the three points. Map out the path followed
A piston/cylinder contains air at 150 psia, 1400 R with a volume of 1.75 ft3. The piston is pressed against the upper stops, (see Fig. P3.14c), and it will float at a pressure of 110 psia. Now the
A setup as in Fig. P3.169 has the R-410a initially at 150 psia, 120 F of mass 0.2 lbm. The balancing equilibrium pressure is 60 psia, and it is now cooled so that the volume is reduced to half of the
The piston/cylinder shown in Fig. P3.169 contains 18 ft3 of R-410a at 300 psia, 300 F. The piston mass and atmosphere gives a pressure of 70 psia that will float the piston. The whole setup cools in
Two rigid tanks are filled with water, as shown in Fig. P3.214. Tank A is 7 ft3 at 1 atm, 280 F and tank B is 11 ft3 at saturated vapor 40 psia. The tanks are connected by a pipe with a closed valve.
A 30-ft-high cylinder, cross-sectional area 1 ft2, has a massless piston at the bottom with water at 70 F on top of it, as shown in Fig. P3.107. Air at 540 R, volume 10 ft3 under the piston is heated
A piston/cylinder arrangement with a linear spring similar to Fig. P3.105 contains R-134a at 60 F, x = 0.6 and a volume of 0.7 ft3. It is heated to 140 F, at which point the specific volume is 0.4413
Water in a piston/cylinder, similar to Fig. P3.225, is at 100◦C, x = 0.5 with mass 1 kg, and the piston rests on the stops. The equilibrium pressure that will float the piston is 300 kPa. The water
A piston/cylinder assembly contains 1 kg of liquid water at 20◦C and 300 kPa. Initially the piston floats, similar to the setup in Problem 3.173, with a maximum enclosed volume of 0.002 m3 if the
A setup like the one in Fig. P3.169 has the R-410a initially at 1000 kPa, 50◦C of mass 0.1 kg. The balancing equilibrium pressure is 400 kPa, and it is now cooled so that the volume is reduced to
Water at 100 kPa and 400 K is heated electrically, adding 700 kJ/kg in a constant-pressure process. Find the final temperature usinga. The water Table B.1b. The ideal-gas Table A.8c. Constant
A gasoline engine has a piston/cylinder with 0.1 kg air at 4 MPa, 1527◦C after combustion, and this is expanded in a polytropic process with n = 1.5 to a volume 10 times larger. Find the expansion
Do the previous problem but do not use constant specific heat.Data from previous problem Air in a piston/cylinder is at 1800 K, 7 MPa and expands in a polytropic process with n = 1.5 to a volume
Air (3 kg) is in a piston/cylinder similar to Fig. P3.5 at 27◦C, 300 kPa. It is now heated to 500 K. Plot the process path in a P–v diagram and find the work and heat transfer in the process.In
Reconsider Problem 3.134, and determine if also using Table B.3 would be more accurate; explain.Data from Problem 3.134,For a special application, we need to evaluate the change in enthalpy for
Repeat Problem 3.134 but use a constant specific heat at the average temperature from the equation in Table A.6 and also integrate the equation in Table A.6 to get the change in enthalpy.Data from
For a special application, we need to evaluate the change in enthalpy for carbon dioxide from 30◦C to 1500◦C at 100 kPa. Do this using the constant specific heat value from Table A.5 and repeat
We want to find the change in u for carbon dioxide between 50◦C and 200◦C at a pressure of 10 MPa. Find it using ideal gas and Table A.5, and repeat using the B section table. TABLE A.5
Estimate the constant specific heats for R-134a from Table B.5.2 at 100 kPa and 125◦C. Compare this to the specific heats in Table A.5 and explain the difference.
Use the ideal-gas air Table A.7 to evaluate the heat capacity Cp at 300 K as a slope of the curve h(T) by Δh/ΔT. How much larger is it at 1000 K and at 1500 K?
The R-410a in Problem 3.14c is at 1000 kPa, 50◦C with a mass of 0.1 kg. It is cooled so that the volume is reduced to half the initial volume. The piston mass and gravitation are such that a
A thermopane window (see Fig. 3.38) traps some gas between the two glass panes. Why is this beneficial?In Figure 3.38
Find the constants in the curve fit for the saturation pressure using Wagner’s correlation, as shown in the previous problem for water and methane. Find other correlations in the literature,
For Tr = 0.7, what is the ratio vg/vf using Fig. D.1 compared to Table D.3? TABLE D.3 Saturated Liquid-Vapor Compressibilities, Lee-Kesler Simple Fluid 0.40 0.70 T, P, sat 0.50 0.60 0.80 0.85 0.90
To solve for v given (P, T) in Eq. 2.14, what is the mathematical problem? RT P = - v - b a (2.14) v? + cbv + db²
Write a program to do the temperature correction on a mercury barometer reading (see Problem 1.70). Input the reading and temperature and output the corrected reading at 20◦C and pressure in
A power plant with a thermal efficiency of 40% is located on a river similar to the arrangement in Fig. P5.61. With a total river mass flow rate of 1 × 105 kg/s at 15◦C, find the maximum power
A heat pump is driven by the work output of a heat engine, as shown in Fig. P5.67. If we assume ideal devices, find the ratio of the total power ˙Q L1 + ˙Q H2 that heats the house to the power from
R-134a fills a 0.1-m3 capsule at 20◦C, 200 kPa. It is placed in a deep freezer, where it is cooled to −10◦C. The deep freezer sits in a room with ambient temperature of 20◦C and has an inside
A constant temperature of −125◦C must be maintained in a cryogenic experiment, although it gains 120 W due to heat transfer. What is the smallest motor you would need for a heat pump absorbing
A proposal is to build a 1000-MW electric power plant with steam as the working fluid. The condensers are to be cooled with river water (see Fig. P5.61). The maximum steam temperature is 550◦C, and
A heat pump is used to heat a house during the winter. The house is to be maintained at 20◦C at all times. When the ambient temperature outside drops to −10◦C, the rate at which heat is lost
A refrigerator should remove 400 kJ from some food. Assume the refrigerator works in a Carnot cycle between −15◦C and 45◦C with a motor compressor of 400 W. How much time does it take if this
An air conditioner provides 1 kg/s of air at 15◦C cooled by outside atmospheric air at 35◦C. Estimate the amount of power needed to operate the air conditioner. Clearly state all assumptions made.
Assume the refrigerator in your kitchen runs in a Carnot cycle. Estimate the maximum COP.
Repeat the previous problem for refrigerants listed in Table A.2 and use the compressibility chart, Fig. D.1, to estimate the pressures.Data from Previous problemThe refrigerant fluid in a household
Locate the state of R-410a at 30 psia,−20 F. Indicate in both the P–v and T–v diagrams the location of the nearest states listed in Table F.10.
Saturated vapor R-410a at 60◦C changes volume at constant temperature. Find the new pressure, and quality if saturated, if the volume doubles. Repeat the problem for the case where the volume is
Plot the atmospheric pressure as a function of elevation (0–20 000 m) at a location where the ground pressure is 100 kPa at 500 m elevation. Use the variation shown in Problem 1.64.Data from
A piston/cylinder with a cross-sectional area of 0.1 ft2 has a piston mass of 200 lbm resting on the stops, as shown in Fig. P1.50. With an outside atmospheric pressure of 1 atm, what should the
Make a control volume around the refrigerator in Fig. 1.3. Identify the mass flow of external air and show where you have significant heat transfer and where storage changes. Heat to room Warm vapor
A car rolls down a hill with a slope such that the gravitational “pull” in the direction of motion is one-tenth of the standard gravitational force (see Problem 1.26). If the car has a mass of
A rigid tank contains 4 kg air at 300◦C, 4 MPa that acts as the hot energy reservoir for a heat engine with its cold side at 20◦C, shown in Fig. P6.99. Heat transfer to the heat engine cools the
The power stroke in an internal combustion engine can be approximated with a poly tropic expansion. Consider air in a cylinder volume of 0.2 L at 7MPa, 1800 K, shown in Fig. P6.111. It now expands in
A cylinder/piston contains saturated vapor R-410a at 10◦C; the volume is 10 L. The R-410a is compressed to 2 MPa, 60◦C in a reversible (internally) poly tropic process. Find the poly tropic
Air goes through a poly tropic process with n = 1.3 in a piston/cylinder setup. It starts at 200 kPa, 300K and ends with a pressure of 2200 kPa. Find the expansion ratio v2/v1, the specific work, and
Consider a heat transfer of 100 kJ from 1500 K hot gases to a steel container at 750 K that has a heat transfer of the 100 kJ out to some air at 375 K. Determine the entropy generation in each of the
A rigid tank has 0.1 kg saturated vapor R-410a at 0◦C that is cooled to −20◦C by a −20◦C heat sink. Show the process in a T–s diagram; find the change in entropy of the R-410a, the heat
One kilogram of water at 500◦C and 1 kg saturated water vapor, both at 200 kPa, are mixed in a constant-pressure and adiabatic process. Find the final temperature and the entropy generation for the
An insulated cylinder/piston contains R-134a at 1MPa, 50◦C, with a volume of 100 L. The R-134a expands, moving the piston until the pressure in the cylinder has dropped to 100 kPa. It is claimed
A rigid tank holds 0.75 kg ammonia at 70◦C as saturated vapor. The tank is now cooled to 20◦C by heat transfer to the ambient at 20◦C. Determine the amount of entropy generation during the
Heat transfer from a 20◦C kitchen to a block of 1.5 kg ice at −10◦C melts it to liquid at 10◦C. How much entropy is generated?
Water in a piston/cylinder is at 101 kPa, 25◦C and mass 0.5 kg. The piston rests on some stops, and the pressure should be 1000 kPa to float the piston. We now heat the water from a 200◦C
A piston/cylinder device keeping a constant pressure has 1 kg water at 20◦C and 1 kg of water at 100◦C, both at 500 kPa separated by a thin membrane, shown in Fig. P6.128. The membrane is broken
Do Problem 6.125 assuming the piston/cylinder is 1.5 kg of steel and has the same temperature as the water at any time.Data from Problem 6.125Water in a piston/cylinder is at 101 kPa, 25◦C and mass
Reconsider problem 3.109 where carbon dioxide is compressed from −20◦C, x = 0.75 to a state of 3 MPa, 20◦C in a piston/cylinder where pressure is linear in volume. Assume heat transfer is from
A closed, rigid container is filled with 1.5 kg water at 100 kPa, 55◦C, 1 kg of stainless steel and 0.5 kg of polyvinyl chloride, both at 20◦Cand 0.1 kg of hot air at 400 K, 100 kPa. It is now
A rigid steel tank of mass 2.5 kg contains 0.5 kg R-410a at 0◦Cwith a specific volume of 0.01m3/kg. The system heats up to the room temperature, 25◦C. Find the process heat transfer and the
A piston/cylinder of total 1 kg steel contains 0.5 kg ammonia at 1600 kPa, both masses at 120◦C. Some stops are placed that so a minimum volume is 0.02 m3, shown in Fig. P6.137. Now the whole
A piston/cylinder contains 0.1 kg water at 500◦C, 1000 kPa. The piston has a stop at half of the original volume, similar to Fig. P6.137. The water now cools to room temperature, 25◦C. Find the
A cylinder/piston arrangement contains 10 g ammonia at 20◦Cwith a volume of 1 L. There are some stops, so if the piston is at the stops, the volume is 1.4 L. The ammonia is now heated to 200◦C by
A cylinder/piston arrangement contains 0.1 kg R-410a of quality x = 0.2534 at −20◦C. Stops are mounted, so Vstop = 3V1, similar to Fig. P6.140. The system is now heated to the final temperature
Air in a rigid tank is at 900 K, 500 kPa, and it now cools to the ambient temperature of 300 K by heat loss to the ambient. Find the entropy generation.
Argon in a light bulb is at 110 kPa, 90◦C. The light is turned off, so the argon cools to the ambient temperature of 20◦C. Disregard the glass and any other mass and find the specific entropy
A spring-loaded piston/cylinder contains 1.5 kg air at 27◦C, 160 kPa. It is now heated in a process in which pressure is linear in volume, P = A + BV, to twice its initial volume, where it reaches
Solve Problem 6.156 using Table A.8.Data from Problem 6.156One kilogram carbon dioxide at 100 kPa, 400 K is mixed with 2 kg carbon dioxide at 200 kPa, 2000 K, in a rigid, insulated tank. Find the
A piston/cylinder contains 1 lbm water at 40 psia, 600 F, and it now cools to 280 F in an isobaric process. The heat goes into a heat engine that rejects heat to the ambient at 77 F and the whole
A cylinder containing R-134a at 60 F, 30 lbf/in.2 has an initial volume of 1 ft3.Apiston compresses the R-134a in a reversible isothermal process until it reaches the saturated vapor state. Calculate
Heat transfer to a block of 3 lbm ice at 15 F melts it to liquid at 50 F in a kitchen. Find the entropy change of the water.
A rigid tank of 1.2 lbm steel contains 1.5 lbm R-134a at 100 F, 80 psia. The tank is placed in a refrigerator that brings it to 0 F. Find the process heat transfer and the combined steel and R-134a
A 5-lbm aluminum radiator holds 2 lbm liquid R-134a at 10 F. The setup is brought indoors and heated with 220 Btu. Find the final temperature and the change in entropy of all the mass.
Air inside a rigid tank is heated from 550 to 600 R. Find the entropy increase s2 − s1. What is the entropy increase if the tank is heated from 2300 to 2350 R?
Helium in a piston/cylinder at 70 F, 20 psia is brought to 720 R in a reversible poly tropic process with exponent n = 1.25. You may assume that helium is an ideal gas with constant specific heat.
Write a program to solve the following problem. One of the gases listed in Table A.6 undergoes a reversible adiabatic process in a cylinder from P1, T1 to P2. We wish to calculate the final
The intercooler in the previous problem uses cold liquid water to cool the nitrogen. The nitrogen flow is 0.1 kg/s, and the liquid water inlet is 20◦C and is setup to flow in the opposite direction
A power plant produces 25 kg/s steam at 3 MPa, 600◦C in the boiler. It cools the condenser with ocean water, so the condenser exit is at 50◦C. A reheat is done at 500 kPa up to 400◦C followed
Notice that the configuration in Fig. 9.29 has the left-hand side column of devices substitute for a compressor in the standard cycle. What is an expression for the equivalent work output from the
Assume the house in the previous problem has a combined 12 000 kg hard wood, 2500 kg gypsum plates (Cp = 1 kJ/kg-K), and 750 kg steel, all of which is at 20◦C. If the air conditioner is turned off,
A gas is represented by the virial EOS with the first two terms, B and C. Find an expression for the work in an isothermal expansion process in a piston/cylinder.
For a PEC fuel cell operating at 350 K, the constants in Eq. 13.29 are ileak = 0.01, iL = 2, i0 = 0.013 all A/cm2, b = 0.08 V, c = 0.1 V, ASR = 0.01 Ω cm2, and EMF = 1.22 V. Find the voltage and the
Assume the SOC fuel cell in the previous problem. How large an area does the fuel cell have to deliver 1 kW with a current density of 1 A/cm2?
A rigid container with volume 200 L is divided into two equal volumes by a partition, shown in Fig. P6.151. Both sides contain nitrogen; one side is at 2 MPa, 200◦C and the other at 200 kPa,
A constant pressure piston/cylinder contains 0.5 kg air at 300 K, 400 kPa. Assume the piston/cylinder has a total mass of 1 kg steel and is at the same temperature as the air at any time. The system
Do Problem 6.152 using Table A.7.Data from Problem 6.152A constant pressure piston/cylinder contains 0.5 kg air at 300 K, 400 kPa. Assume the piston/cylinder has a total mass of 1 kg steel and is at
The air in the tank of Problem 6.88 receives heat transfer from a reservoir at 450 K. Find the entropy generation due to the process from 1 to 3.Data from Problem 6.88Air in a rigid tank is at 100
An insulated cylinder/piston contains R-134a at 150 lbf/in.2, 120 F, with a volume of 3.5 ft3. The R-134a expands, moving the piston until the pressure in the cylinder has dropped to 15 lbf/in.2. It
Heat transfer from a 70 F kitchen to a block of 3 lbm ice at 15 F melts it to liquid at 50 F. Find the entropy generation.

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