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physics
thermodynamics

Questions and Answers of Thermodynamics

Helium has the lowest normal boiling point of any of the elements at 4.2 K. At this temperature the enthalpy of evaporation is 83.3 kJ/kmol. A Carnot refrigeration cycle is analyzed for the
Calculate the amount of work input a refrigerator needs to make ice cubes out of a tray of 0.25 kg liquid water at 10oC. Assume the refrigerator works in a Carnot cycle between –8oC and 35oC with a
A steel bottle V = 0.1 m3 contains R-134a at 20°C, 200 kPa. It is placed in a deep freezer where it is cooled to -20°C. The deep freezer sits in a room with ambient temperature of 20°C and has an
Geothermal underground hot water or steam can be used to generate electric power. Does that violate the second law?
Liquid sodium leaves a nuclear reactor at 800°C and is used as the energy souce in a steam power plant. The condenser cooling water comes from a cooling tower at 15°C. Determine the maximum thermal
A thermal storage is made with a rock (granite) bed of 2 m3 which is heated to 400 K using solar energy. A heat engine receives a QH from the bed and rejects heat to the ambient at 290 K. The rock
A heat engine has a solar collector receiving 0.2 kW per square meter inside which a transfer media is heated to 450 K. The collected energy powers a heat engine which rejects heat at 40oC. If the
Sixty kilograms per hour of water runs through a heat exchanger, entering as saturated liquid at 200 kPa and leaving as saturated vapor. The heat is supplied by a Carnot heat pump operating from a
A heat pump is driven by the work output of a heat engine as shown in figure P7.64. If we assume ideal devices find the ratio of the total power that heats the house to the power from the hot
It is proposed 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. P7.65). The maximum steam temperature is 550°C, and
Two different fuels can be used in a heat engine operating between the fuel burning temperature and a low temperature of 350 K. Fuel A burns at 2200 K delivering 30 000 kJ/kg and costs $1.50/kg. Fuel
A refrigerator keeping 5oC inside is located in a 30oC room. It must have a high temperature ΔT above room temperature and a low temperature ΔT below the refrigerated space in the cycle to actually
A refrigerator uses a power input of 2.5 kW to cool a 5°C space with the high temperature in the cycle as 50°C. The QH is pushed to the ambient air at 35°C in a heat exchanger where the transfer
A house is heated by a heat pump driven by an electric motor using the outside as the low-temperature reservoir. The house loses energy directly proportional to the temperature difference as Q̇loss
A car engine takes atmospheric air in at 20oC, no fuel, and exhausts the air at –20oC producing work in the process. What do the first and the second laws say about that?
A farmer runs a heat pump with a motor of 2 kW. It should keep a chicken hatchery at 30oC which loses energy at a rate of 0.5 kW per degree difference to the colder ambient. The heat pump has a
Consider a Carnot cycle heat engine operating in outer space. Heat can be rejected from this engine only by thermal radiation, which is proportional to the radiator area and the fourth power of
A house is heated by an electric heat pump using the outside as the low-temperature reservoir. For several different winter outdoor temperatures, estimate the percent savings in electricity if the
A house is cooled by an electric heat pump using the outside as the high-temperature reservoir. For several different summer outdoor temperatures, estimate the percent savings in electricity if the
A heat pump has a coefficient of performance that is 50% of the theoretical maximum. It maintains a house at 20°C, which leaks energy of 0.6 kW per degree temperature difference to the ambient. For
An air conditioner cools a house at TL = 20°C with a maximum of 1.2 kW power input. The house gains 0.6 kW per degree temperature difference to the ambient and the refrigeration COP is β = 0.6
A Carnot heat engine, shown in Fig. P7.76, receives energy from a reservoir at Tres through a heat exchanger where the heat transferred is proportional to the temperature difference as = K(Tres -
Hydrogen gas is used in a Carnot cycle having an efficiency of 60% with a low temperature of 300 K. During the heat rejection the pressure changes from 90 kPa to 120 kPa. Find the high and low
An ideal gas Carnot cycle with air in a piston cylinder has a high temperature of 1200 K and a heat rejection at 400 K. During the heat addition the volume triples. Find the two specific heat
Air in a piston/cylinder goes through a Carnot cycle with the P-v diagram shown in Fig. 7.24. The high and low temperatures are 600 K and 300 K respectively. The heat added at the high temperature is
A windmill produces power on a shaft taking kinetic energy out of the wind. Is it a heat engine? Is it a perpetual machine? Explain.
A car engine operates with a thermal efficiency of 35%. Assume the air-conditioner has a coefficient of performance of β = 3 working as a refrigerator cooling the inside using engine shaft work to
An air-conditioner with a power input of 1.2 kW is working as a refrigerator (β = 3) or as a heat pump (β′ = 4). It maintains an office at 20°C year round which exchanges 0.5 kW per degree
A rigid insulated container has two rooms separated by a membrane. Room A contains 1 kg air at 200oC and room B has 1.5 kg air at 20oC, both rooms at 100 kPa. Consider two different cases 1) Heat
At certain locations geothermal energy in undergound water is available and used as the energy source for a power plant. Consider a supply of saturated liquid water at 150°C. What is the maximum
We wish to produce refrigeration at −30°C. A reservoir, shown in Fig. P7.84, is available at 200°C and the ambient temperature is 30°C. Thus, work can be done by a cyclic heat engine operating
A 4L jug of milk at 25°C is placed in your refrigerator where it is cooled down to 5°C. The high temperature in the Carnot refrigeration cycle is 45°C and the properties of milk are the same as
A combination of a heat engine driving a heat pump (see Fig. P7.86) takes waste energy at 50°C as a source Qw1 to the heat engine rejecting heat at 30°C. The remainder Qw2 goes into the heat pump
Air in a rigid 1 m3 box is at 300 K, 200 kPa. It is heated to 600 K by heat transfer from a reversible heat pump that receives energy from the ambient at 300 K besides the work input. Use constant
Consider the rock bed thermal storage in Problem 7.61. Use the specific heat so you can write dQH in terms of dTrock and find the expression for dW out of the heat engine. Integrate this expression
A heat pump heats a house in the winter and then reverses to cool it in the summer. The interior temperature should be 20°C in the winter and 25°C in the summer. Heat transfer through the walls and
Ice cubes in a glass of liquid water will eventually melt and all the water approach room temperature. Is this a reversible process? Why?
A furnace, shown in Fig. P7.90, can deliver heat, QH1 at TH1 and it is proposed to use this to drive a heat engine with a rejection at Tatm instead of direct room heating. The heat engine drives a
A 10-m3 tank of air at 500 kPa, 600 K acts as the high-temperature reservoir for a Carnot heat engine that rejects heat at 300 K. A temperature difference of 25°C between the air tank and the Carnot
Does Clausius say anything about the sign for ϕ dQ ?
Saturated water vapor at 200 kPa is compressed to 600 kPa in a reversible adiabatic process. Find the new v and T.
Argon in a light bulb is at 90 kPa and heated from 20oC to 60oC with electrical power. Do not consider any radiation, nor the glass mass. Find the total entropy generation per unit mass of argon.
We wish to obtain a supply of cold helium gas by applying the following technique. Helium contained in a cylinder at ambient conditions, 100 kPa, 20°C, is compressed in a reversible isothermal
A 1-m3 insulated, rigid tank contains air at 800 kPa, 25°C. A valve on the tank is opened, and the pressure inside quickly drops to 150 kPa, at which point the valve is closed. Assuming that the air
Nitrogen at 200oC, 300 kPa is in a piston cylinder, volume 5 L, with the piston locked with a pin. The forces on the piston require a pressure inside of 200 kPa to balance it without the pin. The pin
A rigid container with Volume 200 L is divided into two equal Volumes by a partition, shown in Fig. P8.104. Both sides contain nitrogen, one side is at 2 MPa, 200°C, and the other at 200 kPa,
Nitrogen at 600 kPa, 127°C is in a 0.5 m3 insulated tank connected to a pipe with a valve to a second insulated initially empty tank of volume 0.5 m3, shown in Fig. P8.105. The valve is opened and
Neon at 400 kPa, 20°C is brought to 100°C in a polytropic process with n = 1.4. Give the sign for the heat transfer and work terms and explain.
A mass of 1 kg of air contained in a cylinder at 1.5 MPa, 1000 K, expands in a reversible adiabatic process to 100 kPa. Calculate the final temperature and the work done during the process, using a.
An ideal gas having a constant specific heat undergoes a reversible polytropic expansion with exponent, n = 1.4. If the gas is carbon dioxide will the heat transfer for this process be positive,
A cylinder/piston contains 1 kg methane gas at 100 kPa, 20°C. The gas is compressed reversibly to a pressure of 800 kPa. Calculate the work required if the process is a. Adiabatic. b. Isothermal c.
A computer chip dissipates 2 kJ of electric work over time and rejects that as heat transfer from its 50oC surface to 25oC air. How much entropy is generated in the chip? How much if any is generated
Helium in a piston/cylinder at 20°C, 100 kPa is brought to 400 K in a reversible polytropic process with exponent n = 1.25. You may assume helium is an ideal gas with constant specific heat. Find
The power stroke in an internal combustion engine can be approximated with a polytropic expansion. Consider air in a cylinder Volume of 0.2 L at 7 MPa, 1800 K, shown in Fig. P8.111. It now expands in
A piston/cylinder contains air at 300 K, 100 kPa. It is now compressed in a reversible adiabatic process to a volume 7 times as small. Use constant heat capacity and find the final pressure and
A cylinder/piston contains carbon dioxide at 1 MPa, 300°C with a volume of 200 L. The total external force acting on the piston is proportional to V3. This system is allowed to cool to room
A device brings 2 kg of ammonia from 150 kPa, -20oC to 400 kPa, 80oC in a polytropic process. Find the polytropic exponent, n, the work and the heat transfer. Find the total entropy generated
A cylinder/piston contains 100 L of air at 110 kPa, 25°C. The air is compressed in a reversible polytropic process to a final state of 800 kPa, 200°C. Assume the heat transfer is with the ambient
A mass of 2 kg ethane gas at 500 kPa, 100°C, undergoes a reversible polytropic expansion with exponent, n = 1.3, to a final temperature of the ambient, 20°C. Calculate the total entropy generation
A piston/cylinder contains air at 300 K, 100 kPa. A reversible polytropic process with n = 1.3 brings the air to 500 K. Any heat transfer if it comes in is from a 325oC reservoir and if it goes out
A cylinder/piston contains saturated vapor R-22 at 10°C; the volume is 10 L. The R-22 is compressed to 2 MPa, 60°C in a reversible (internally) polytropic process. If all the heat transfer during
A cylinder/piston contains air at ambient conditions, 100 kPa and 20°C with a volume of 0.3 m3. The air is compressed to 800 kPa in a reversible polytropic process with exponent, n = 1.2, after
A car uses an average power of 25 hp for a one hour round trip. With a thermal efficiency of 35% how much fuel energy was used? What happened to all the energy? What change in entropy took place if
A reversible heat pump uses 1 kW of power input to heat a 25oC room, drawing energy from the outside at 15oC. Assuming every process is reversible, what are the total rates of entropy into the heat
An amount of power, say 1000 kW, comes from a furnace at 800°C going into water vapor at 400°C. From the water the power goes to a solid metal at 200°C and then into some air at 70°C. For each
Room air at 23oC is heated by a 2000 W space heater with a surface filament temperature of 700 K, shown in Fig. P8.122. The room at steady state looses the power to the outside which is at 7oC. Find
A small halogen light bulb receives an electrical power of 50 W. The small filament is at 1000 K and gives out 20% of the power as light and the rest as heat transfer to the gas, which is at 500 K;
A farmer runs a heat pump using 2 kW of power input. It keeps a chicken hatchery at a constant 30oC while the room loses 10 kW to the colder outside ambient at 10oC. What is the rate of entropy
The automatic transmission in a car receives 25 kW shaft work and gives out 24 kW to the drive shaft. The balance is dissipated in the hydraulic fluid and metal casing, all at 45oC, which in turn
An insulated cylinder/piston has an initial volume of 0.15 m3 and contains steam at 400 kPa, 200oC. The steam is expanded adiabaticly, and the work output is measured very carefully to be 30 kJ. It
A closed tank, V = 10 L, containing 5 kg of water initially at 25°C, is heated to 175°C by a heat pump that is receiving heat from the surroundings at 25°C. Assume that this process is reversible.
Two tanks contain steam, and they are both connected to a piston/cylinder as shown in Fig. P8.128. Initially the piston is at the bottom and the mass of the piston is such that a pressure of 1.4 MPa
A piston/cylinder with constant loading of piston contains 1 L water at 400 kPa, quality 15%. It has some stops mounted so the maximum possible volume is 11 L. A reversible heat pump extracting heat
A liquid is compressed in a reversible adiabatic process. What is the change in T?
Water in a piston/cylinder is at 1 MPa, 500°C. There are two stops, a lower one at which Vmin = 1 m3 and an upper one at Vmax = 3 m3. The piston is loaded with a mass and outside atmosphere such
A cylinder fitted with a frictionless piston contains water. A constant hydraulic pressure on the back face of the piston maintains a cylinder pressure of 10 MPa. Initially, the water is at 700°C,
A cylinder/piston contains 3 kg of water at 500 kPa, 600°C. The piston has a cross-sectional area of 0.1 m2 and is restrained by a linear spring with spring constant 10 kN/m. The setup is allowed to
An insulated cylinder fitted with a frictionless piston contains saturated vapor R-12 at ambient temperature, 20°C. The initial volume is 10 L. The R-12 is now expanded to a temperature of -30°C.
A piston/cylinder assembly contains 2 kg of liquid water at 20°C, 100 kPa and it is now heated to 300°C by a source at 500°C. A pressure of 1000 kPa will lift the piston off the lower stops. Find
An uninsulated cylinder fitted with a piston contains air at 500 kPa, 200°C, at which point the volume is 10 L. The external force on the piston is now varied in such a manner that the air expands
A cylinder fitted with a piston contains 0.5 kg of R-134a at 60°C, with a quality of 50 percent. The R-134a now expands in an internally reversible polytropic process to ambient temperature, 20°C
A cylinder with a linear spring-loaded piston contains carbon dioxide gas at 2 MPa with a volume of 50 L. The device is of aluminum and has a mass of 4 kg. Everything (Al and gas) is initially at
A vertical cylinder/piston contains R–22 at −20°C, 70% quality, and the volume is 50 L, shown in Fig. P8.138. This cylinder is brought into a 20°C room, and an electric current of 10 A is
A gas in a rigid vessel is at ambient temperature and at a pressure, P1, slightly higher than ambient pressure, P0. A valve on the vessel is opened, so gas escapes and the pressure drops quickly to
Two 5 kg blocks of steel, one at 250oC the other at 25oC, come in thermal contact. Find the final temperature and the total entropy generation in the process?
One kg of air at 300 K is mixed with one kg air at 400 K in a process at a constant 100 kPa and Q = 0. Find the final T and the entropy generation in the process.
One kg of air at 100 kPa is mixed with one kg air at 200 kPa, both at 300 K, in a rigid insulated tank. Find the final state (P, T) and the entropy generation in the process.
An ideal gas goes through a constant T reversible heat addition process. How do the properties (v, u, h, s, P) change (up, down or constant)?
Carbon dioxide is compressed to a smaller volume in a polytropic process with n = 1.2. How do the properties (u, h, s, P, T) change (up, down or constant)?
Hot combustion air at 1500 K expands in a polytropic process to a volume 6 times as large with n = 1.5. Find the specific boundary work and the specific heat transfer.
When a substance has completed a cycle v, u, h and s are unchanged. Did anything happen? Explain.
A window receives 200 W of heat transfer at the inside surface of 20oC and transmits the 200 W from its outside surface at 2oC continuing to ambient air at –5oC. Find the flux of entropy at all
Consider the steam power plant in Example 6.9 and assume an average T in the line between 1 and 2. Show that this cycle satisfies the inequality of Clausius.
Assume the heat engine in Problem 7.25 has a high temperature of 1200 K and a low temperature of 400 K. What does the inequality of Clausius say about each of the four cases?
Let the steam power plant in Problem 7.26 have 700oC in the boiler and 40oC during the heat rejection in the condenser. Does that satisfy the inequality of Clausius? Repeat the question for the cycle
A heat engine receives 6 kW from a 250oC source and rejects heat at 30oC. Examine each of three cases with respect to the inequality of Clausius.a.b.c. Carnot cycle
Examine the heat engine given in Problem 7.50 to see if it satisfies the inequality of Clausius.
Find the entropy for the following water states and indicate each state on a T-s diagram relative to the two-phase region. a. 250oC, v = 0.02 m3/kg b. 250oC, 2000 kPa c. –2oC, 100 kPa d. 20oC, 100
Find the missing properties and give the phase of the substance a. H2O s = 7.70 kJ/kg K, P = 25 kPa h = ? T = ? x = ? b. H2O u = 3400 kJ/kg, P = 10 MPa T = ? x = ? s = ? c. R-12 T = 0°C, P = 200 kPa
Saturated liquid water at 20oC is compressed to a higher pressure with constant temperature. Find the changes in u and s when the final pressure isa. 500 kPab. 2000 kPac. 20 000 kPa

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