Section-1: Simple Processes Involving Closed Uniform Systems

• Constant Volume Processes
Determine (a) the amount of heat necessary to raise the temperature of 1 kg of aluminum from 30oC to 100oC. (b) What-if scenario: How would the answer in part (a) change if the working substance was wood instead of aluminum? [Manual Solution] [TEST Solution] 		Click on the image to animate!
Answers: (a) 63 kJ, (b) 123.2 kJ

Suppose the aluminum block in the above problem was heated by a reservoir (TER) at 200°C. Determine (a) the change in entropy of the block, and (b) the entropy that is transferred from the reservoir. (c) How do you account for the discrepancy between the two results? (d) What-if scenario: How would the answers in parts (a) and (b) affected if the reservoir was at 500°C? [Manual Solution] [TEST Solution] 		 
Answers: (a) 0.187 kJ/K, (b) 0.133 kJ/K, (d) 0.187 kJ/K, 0.082 kJ/K,  

A block of iron (specific heat: 0.45 kJ/kg.K) with a mass of 20 kg is heated from its initial temperature of 10oC to a final temperature of 200oC by keeping it in thermal contact with a thermal energy reservoir (TER) at 300oC. All other faces of the block are completely insulated. Determine the amount of (a) heat and (b) entropy transfer from the reservoir. (c) Also calculate the entropy generated in the system's universe due to this heat transfer. [Manual Solution] [TEST Solution] 		Click on the image to animate!
Answers: (a) 1710 kJ, (b) 2.984 KJ/K, (c) 1.637 kJ/K

A block of aluminum with m = 0.5 kg, T = 20oC is dropped into a reservoir at a temperature 90oC. Calculate (a) the change in stored energy, (b) the amount of heat transfer, (c) the change in entropy, (d) the amount of entropy transfer by heat, and (e) the entropy generation in the system's universe during the heat transfer process. [Manual Solution] [TEST Solution] 		 
Answers: (a) 31.5 kJ, (b) 31.5 kJ, (c) 0.0964 kJ/K, (d) 0.0868 kJ/K, (e) 0.0096 kJ/K  

A 0.8 m3 rigid tank initially contains refrigerant-12 in the saturated vapor form at 0.9 MPa. As a result of heat transfer from refrigerant, the pressure drops to 250 kPa. Determine (a) the final temperature, (b) the amount of refrigerant that condenses, and (c) the heat transfer. [Manual Solution] [TEST Solution]
Click on the image to animate!
Answers: (a) -6.27 oC, (b) 29.69 kg, (c) -4787.12 kJ

A rigid tank of volume 50 m3 contains superheated steam at 100 kPa, 200oC. The tank is allowed to cool down to the atmospheric temperature of 10oC. Determine (a) the final pressure, (b) the heat transfer, (c) the change in entropy of steam, and (d) the entropy generation in the tank's universe. (e) What-if scenario: How would the answer in part (a) change if the steam was initially at 500 kPa? [Manual Solution] [TEST Solution]
Answers: (a) 1.23 kPa, (b) -59.1 MJ, (c) 172.7 kJ/K, (d) 36.03 kJ/K, (e) No Change

A rigid tank of volume 10 m3 contains superheated steam at 1 MPa and 400 deg-C. Due to heat loss to the outside atmosphere, the tank gradually cools down to the atmospheric temperature of 25 deg-C. Determine (a) the heat transfer, and (b) the entropy generated in the system’s universe during this cooling process. (c) Plot how the pressure changes as temperature decreases during the process (pressure vs. temperature plot). (d) Can you explain the discontinuity in the plot? [Manual Solution] [TEST Solution]
Answers: (a) -92.54 MJ, (b) 80.825 kJ/K

A rigid tank contains 3.2 kg of refrigerant-134a initially at 26oC and 140 kPa. The refrigerant is now cooled until its pressure drops to 100 kPa. Determine (a) the entropy change of the refrigerant, (b) the entropy transfer to a reservoir at -50oC, and (c) the entropy generation in the universe due to the process. [Manual Solution] [TEST Solution]
Answers: (a) -0.754 kJ/K, (b) 0.889 kJ/K, (c) 0.134 kJ/K

A steam radiator (used for space heating) has a volume of 20 L and is filled up with steam at 200 kPa and 250oC. Now the inlet and exit ports are closed. As the radiator cools down to a room temperature of 20o C, determine (a) the heat transfer and show the process on a p-v diagram. (b) What-if scenario: How would the answer in part (a) change if the steam pressure in the radiator was 400 kPa instead? [Manual Solution] [TEST Solution]
Answers: (a) -43.4kJ, (b) -88kJ

A steam radiator has a volume of 25 L and is filled up with steam at 350 kPa and 280oC. Now the inlet and exit ports are closed. As the radiator pressure drops down to 180 kPa, determine (a) the heat transfer and show the process on a p-v diagram. (b) What-if scenario: How would the answer in part (a) change if the steam pressure in the radiator was 500 kPa instead? [Manual Solution] [TEST Solution] Click on the image to animate!
Answers: (a) -27.09 kJ, (b) -61.3 kJ

The radiator of a steam heating system has a volume of 15 L and is filled with super heated water vapor at 225 kPa and 230oC. Now the inlet and exit ports are closed. After a while the temperature of the steam drops to 88o as a result of heat transfer to the room air. Determine (a) the heat transfer, (b) and the entropy change of the steam during this process. [Manual Solution] [TEST Solution]
Answers: (a) -21.66 kJ, (b) -0.056 kJ/K

A steam radiator has a volume of 20 L and is filled up with steam at 200 kPa and 250oC. Now the inlet and exit ports are closed. As the radiator cools down to a room temperature of 20oC, determine (a) the final pressure, and (b) the entropy generated in the universe. [Manual Solution] [TEST Solution]
Answers: (a) 2.34 kPa, (b) 0.025 kJ/K

A well-insulated rigid tank contains 6 kg of saturated liquid vapor mixture of water at 150 kpa. Initially, half of the mass is in liquid phase. An electric resistance heater placed in the tank is now turned on and kept on until all the liquid is vaporized. Determine (a) the electrical work, (b) the entropy change of the steam during this process, and (c) the entropy generated in the system's universe. [Manual Solution] [TEST Solution]
Click on the image to animate!
Answers:(a) -6.31 MJ, (b) 15.89 kJ/K, (c) 15.89 kJ/K

A 0.4 m3 rigid tank contains refrigerant-134a initially at 250 kPa and 45 percent quality. Heat is transferred now to the refrigerant from a source at 37oC until pressure rises to 420 kPa. Determine (a) the entropy change of the refrigerant, (b) the entropy change of the heat source, and (c) the total entropy generation in the universe due to the process. [Manual Solution] [TEST Solution]
Answers: (a) 2.5667 kJ/K, (b) 2.286 kJ/K, (c) 0.2804 kJ/K

A rigid tank with 3 kg of H2O at 150 kPa, x = 0.2 is heated with 1000 kJ. Determine (a) the final pressure, (b) phase composition of H2O. (c) What-if scenario: How would the answer in part (a) change if the tank was heated with 500 kJ? [Manual Solution*] [TEST Solution]
Click on the image to animate!
Answers: (a) 260 kPa, (b) Saturated Mixture, (c) 202 kPa

A rigid tank contains 1 kg of H2O at 100 kPa, x = 0.1. Given that the tank can withstand a maximum internal pressure of 5 MPa, determine (a) the maximum temperature to which the steam in the tank can be heated, and (b) the amount of heat transfer necessary to reach the critical pressure. [Manual Solution] [TEST Solution]
Answers: (a) 1567 oC, (b) 4621 kJ

An insulated rigid tank contains 1.5 kg of helium at 30oC and 500 kPa. A paddle wheel with a power rating of 0.1 kW is operated within the tank for 30 minutes. Determine (a) the final temperature, (b) pressure, (c) and the entropy generated in the tank. [Manual Solution] [TEST Solution] 		Click on the image to animate!

Answers: (a) 68.5 oC, (b) 563 kPa, (c) 0.559 kJ/K

A 2 m3 insulated rigid tank contains 3 kg of carbon dioxide at 110 kPa. Now paddle wheel work is done on the system until the pressure in the tank rises to 127 kPa. Determine (a) the entropy change of carbon dioxide, (b) work done by paddle wheel, and (c) the entropy generated in the tank and its immediate surroundings. Use the PG model. (d) What-if scenario: How would the answer in part (b) change if the IG model was used instead? [Manual Solution] [TEST Solution]

Answers: (a) 0.282 kJ/K, (b) -117.8 kJ, (c) 0.282 (d) -137.6 kJ

Air is contained in an insulated, rigid volume at 25oC and 180 kPa. A paddle wheel, inserted in the volume, does 800 kJ of work on air. If the volume is 2m3, determine (a) the entropy increase, (b) final pressure, and (c) temperature. Use the IG model for air. [Manual Solution] [TEST Solution]

Answers: (a) 1.92 kJ/K, (b) 335.6 kPa, 282.7oC

A person living in a 4m x 5m x 5m room turns on a 100-W fan before he leaves the warm room at 100 kPa, 30oC, hoping that the room will be cooler when he comes back after 5 hours. Disregarding any heat transfer and using the PG model for air, determine (a) the temperature he discovers when he comes back. (b) What-if scenario: How would the answer in part (a) change if the fan power was 50 W instead? [Manual Solution] [TEST Solution] 		Click on the image to animate!
Answers: (a) 51.8oC, (b) 40.9oC

• Pressure Regulated Processes (Sec-1 Continued)
A piston-cylinder device contains 0.01 kg of steam at a pressure of 100 kPa and a quality of 10%. Determine the heat transfer necessary to improve the quality to 100% when heating is carried out (a) in a constant pressure manner by allowing the piston to move freely, or (b) in a constant volume manner by locking the piston in its initial position. [ Manual Solution] [TEST Solution] 		 
Answers: (a) 20.32 kJ, (b) 19.61 kJ  

A mass of 10 kg of saturated water vapor at 300 kPa is heated at constant pressure until the temperature reaches 500oC. Calculate (a) the work done by the steam during the process, and (b) the amount of heat transfer. (c) What-if scenario: How would the answer in part (b) change if the pressure remained constant at 600 kPa? [Manual Solution] [TEST Solution] 		Click on the image to animate!
Answers: (a) 1742.56 kJ, (b) 7606 kJ, (b) -37.44 kJ

In problem , determine the minimum average value of the boundary temperature for which the second law is not violated. [Manual Solution*] [TEST Solution]  
Answers: 297.4°C  

A vertical piston-cylinder assembly (see Anim. ) contains 10 L of air at 20oC. The cylinder has an internal diameter of 20 cm. The piston is 2 cm thick and is made of steel of density 7830 kg/m3. If the atmospheric pressure outside is 101 kPa, determine the (a) heat and (b) work transfer during the process. (c) What-if scenario: How would the answers change if the piston weight was neglected? [Manual Solution] [Test Solution] 		 
Answers: (a) 3.585 kJ, (b) 1.025 kJ, (c) 3.53 kJ, 1.01 kJ  

A frictionless piston-cylinder device contains 0.1 kg of refrigerant-12 as a saturated liquid. The piston is free to move, and its mass is such that it maintains a pressure of 200 kPa on the refrigerant. Due to heat transfer from the atmosphere, the temperature of the refrigerant gradually rises to the atmospheric temperature of 25oC. Calculate (a) the work transfer, (b) the heat transfer, (c) the change of entropy of the refrigerant, and (d) the entropy generated in the system's universe. [Manual Solution] [TEST Solution]
Answers: (a) 1.95 kJ, (b) 18.1 kJ, (c) 0.0688 kJ/K, (d) 0.0081 kJ/K

A mass of 2 kg of liquid water is completely vaporized at a constant pressure of 1 atm. Determine (a) the heat added. (b) What-if scenario: How would the answer change if the pressure was 2 atm? [Manual Solution] [TEST Solution]

Answers: (a) 4514 kJ, (b) 4402kJ

A frictionless piston is used to provide a constant pressure of 500 kPa in a cylinder containing steam originally at 250oC with a volume of 3 m3. Determine (a) the final temperature if 3000 kJ of heat is added, (b) the work done by piston. [Manual Solution] [Test Solution]
Answers: (a) 477oC , (b) 680 kJ

A piston-cylinder device initially contains 2 kg of liquid water at 140 kPa and 25oC. The water is now heated at a constant pressure by addition of 3600 kJ of heat. Determine (a) the final temperature, (b) the entropy change of the water during this process, and (c) the boundary work. [Manual Solution] [TEST Solution]
Answers: (a) 109.2oC, (b) 9.65 kJ/K, (c) 224.2 kJ

A frictionless piston-cylinder device contains liquid-vapor mixture of water at 100oC. During a constant pressure process, 700 kJ of heat is transferred to the surrounding air at 25oC. As a result, part of the water vapor contained in the cylinder condenses. Determine (a) the entropy change of the water, and (b) the total entropy generated during this heat transfer process. [Manual Solution*] [TEST Solution] 		Click on the image to animate!
Answers: (a) -1.87 kJ/K, (b) 0.472 kJ/K

A frictionless piston-cylinder device contains 10 kg of superheated vapor at 550 kPa and 340 oC. Steam is now cooled at constant pressure until 60 percent of it, by mass, condenses. Determine (a) the work done during the process. (b) What-if scenario: How would the answer in (a) change if steam is cooled at constant pressure until 80 percent of it, by mass, condenses. [Manual Solution] [TEST Solution]
Answers: (a) -2041.42 kJ, (b) -2417.93 kJ

A piston-cylinder device contains 8 kg of refrigerant-134a at 850 kPa and 70 oC. The refrigerant is now cooled at constant pressure until it comes to thermal equilibrium with the atmosphere, which is at 20oC. Determine the amount of (a) heat transfer, (b) entropy transfer into the atmosphere, (c) the change of entropy of the refrigerant, and (d) the entropy generated in the system's universe. [Manual Solution] [TEST Solution] 		 
Answers: (a) -1814.5 kJ, (b) -6.191 kJ/K, (c) -5.875 kJ/K, (d) 0.211 kJ/K  

An insulated piston-cylinder device contains 3 L of saturated liquid water at a constant pressure 180 kPa. An electric resistance heater inside the cylinder is now turned on, and 2000 kJ of energy is transferred to the steam. Determine (a) final temperature, (b) the boundary work, and (c) entropy change of water in this process. [Manual Solution*] [TEST Solution] 		Click on the image to animate!
Answers: (a) 355 kPa, (b) 139.39o C, (c) 46.6 kJ

A piston-cylinder device initially contains 20 g of saturated water vapor at 300 kPa. A resistance heater is operated within the cylinder with a current of 0.4 A from a 240 V source until the volume doubles. At the same time a heat loss of 4 kJ occurs. Determine (a) the final temperature, (b) duration of the process. (c) What-if scenario: How would the answer in part (a) change if the piston-cylinder device initially contained saturated water? [Manual Solution] [TEST Solution] 		 
Answers: (a) 516.1oC, (b) 207 sec, (c) 133.5oC

An insulated container contains a block of ice of mass 1 ton (US) at 0oC. The insulation is removed, and the ice gradually melts to water and comes to thermal equilibrium with the surroundings at 25°C. Assuming the pressure to remain constant at 100 kPa, determine (a) the boundary work, and (b) the heat transfer during the process. (c) What-if scenario: By what percentage will the heat transfer increase if the initial temperature of the ice block was -25°C? [Manual Solution] [TEST Solution] 		Click on the image to animate!
Answers: (a) -7.95 kJ, (b) 397.6 MJ, (c) 11.47%

In the problem described above, determine (a) the change of entropy of the system, (b) the entropy transfer from the surroundings, and (c) the entropy generation in the system's universe during the process. (d) [Manual Solution] [TEST Solution] 		 
Answers: (a) 1441 kJ/K, (b) 1334 kJ/K, (c) 107.28 kJ/K  

• Temperature Regulated Processes
A mass of 1.5 kg of air at 160 kPa and 15 oC is contained in a gas-tight, frictionless piston-cylinder device. The air is now compressed to a final pressure of 650 kPa. During the process heat is transferred from the air such that the temperature inside the cylinder remains constant. (a) Calculate the work done during this process. Use the PG model for air. (b) What-if scenario: How would the answer change if the IG model was used? [Manual Solution] [TEST Solution] 		Click on the image to animate!
Answers: (a) -173.88 kJ, (b) No change

In the above problem determine (a) the change of entropy of the air, (b) the entropy transferred into the atmosphere at 10 °C, and (c) the entropy generation in the system's universe during the compression process. [Manual Solution*] [TEST Solution]
Answers: (a) -0.6035 kJ/K, (b) 0.5834 kJ/K, (c) 0.0107 kJ/K

Nitrogen at an initial state of 80oF, 25 psia and 6 ft3 is pressed slowly in an isothermal process to a final pressure of 110 psia. Determine (a) the work done during the process. (b) What-if scenario: How would the answer change if pressure was 100 psia? [Manual Solution] [TEST Solution]
Answers: (a) -41.3 Btu, (b) -10.58 Btu

• Reversible and Irreversible Processes (Sec-1 Continued)
An insulated piston-cylinder device contains 0.04 m3 of steam at 300 kPa and 200oC. Steam is now compressed in a reversible manner to a pressure of 1 MPa. Calculate (a) the work done. (c) What-if scenario: How would the answer change if the initial temperature was 800oC? [Manual Solution] [TEST Solution] 		Click on the image to animate!
Answers: (a) -12.83 kJ, (b) -13.20 kJ

Air at 20oC, 95 kPa is compressed in a piston-cylinder device of volume 1 L in a frictionless and adiabatic manner. If the volumetric compression ratio is 10, determine (a) the final temperature, (b) the boundary work transfer. Use the PG model for air. (c) What-if scenario: How would the answer in part (b) change if the initial temperature was 45o? [Manual Solution*] [TEST Solution] 		 
Answers: (a) 464oC, (b) -0.36 kJ, (c) 526oC, -0.36 kJ

A piston-cylinder device initially contains 10 ft3 of argon gas at 25 psia and 70oF. Argon is now compressed in a polytropic process (pVn = constant) to 70 psia and 300oF. Determine (a) if the process is reversible, impossible or irreversible. (b) Also determine the change of entropy for argon. [Manual Solution] [TEST Solution]
Answers: (a) Impossible, (b,c) -0.021 kJ/K  

A piston-cylinder device initially contains 0.8 kg of O2 at 100 kPa and 27oC. It is now compressed in a polytropic process (pV1.3 = constant) to half the original volume. Determine (a) the change of entropy for the system, (b) entropy transfer to the surroundings (at 27oC), and (c) the entropy generated in the system's universe due to this process. (d) What-if scenario: How would the answer in part (c) change if the surrounding temperature was 0oC? [Manual Solution] [TEST Solution] 		Click on the image to animate!
Answers: (a) 0.0370, (b) 0.0411 kJ/K, (c) 0.0041 kJ/K, (d) 0.0082 kJ/K

A cylinder fitted with a piston has an initial volume of 0.1 m3 and contains nitrogen at 100 kPa, 25oC. The piston is moved, compressing the nitrogen until the pressure is 1.5 MPa and the temperature is 200oC. During this compression process heat is transferred from nitrogen to the atmosphere at 25oC, and the work done on the nitrogen is 30 kJ. Determine (a) the amount of this heat transfer, (b) the change in entropy of nitrogen, (c) the amount of entropy transferred into the atmosphere, and (d) the entropy generation during the process. Use the PG model for nitrogen. [Manual Solution] [TEST Solution]
Answers: (a) -15.49 kJ, (b) -0.0370 kJ/K, (c) 0.0519 kJ, (d) 0.0149 kJ/K

A rubber ball of mass m is dropped from a height h on a rigid floor. It bounces back and forth and finally comes to rest on the floor. What is the entropy generation in the universe due to this irreversible phenomenon? Assume the atmospheric temperature to be T0. [Manual Solution]
Answers: mgh/(1000To) kJ/K

• Sequential Processes (Sec-1 Continued)
A piston-cylinder device contains 40 kg of water at 150 kPa and 30o C. The cross-sectional area of the piston is 0.1 m2. Heat is now added causing part of the water to evaporate. When the volume reaches 0.2 m3, the piston reaches a linear spring with a spring constant of 120 kN/m. More heat is added until the piston moves by another 25 cm. Determine (a) the final pressure, (b) temperature, and (c) the total heat transfer. [Manual Solution] [TEST Solution] 		Click on the image to animate!
Answers: (a) 450 kPa, (b) 147.9o C, (c) 82.1 MJ

A piston-cylinder device contains 40 kg of water at 150 kPa and 30o C. The cross-sectional area of the piston is 0.1 m2. Heat is now added causing part of the water to evaporate. When the volume reaches 0.2 m3, the piston reaches a spring with a constant spring constant. More heat is added until the volume increases to 0.3 m3 and the pressure increases to 1.35 MPa. Determine (a) the spring constant, (b) the final temperature, and (c) the total heat transfer. [Manual Solution] [TEST Solution]
Answers: (a) 120 kN/m, (b) 193.4o C, (c) 31.0 MJ

If the heat addition takes place from a source at 500oC during the entire process in the above problem, determine (a) the change of entropy of the steam, (b) entropy transfer from the source, and (c) entropy generated in the universe during the process. [Manual Solution] [TEST Solution]
Answers: (a) 80.64 kJ/K, (b) 40.13 kJ/K, (c) 40.50 kJ/K o C, (c) 31.0 MJ

A mass of 10 kg of saturated liquid-vapor mixture of R-12 is contained in a piston-cylinder device at 0oC. Initially half of the mixture is in the liquid phase. Heat is now transferred, and the piston, which is resting on a stop-ring, starts moving when the pressure reaches 500 kPa. Heat transfer continues until the total volume doubles. Determine (a) the final pressure, (b) work, and (c) heat transfer in the entire process. Also, show the process on a p-v diagram. [Manual Solution] [TEST Solution] 		Click on the image to animate!
Answers: (a) 500 kPa, (b) 140.3kJ, (c) 1688.3 kJ

An insulated cylinder with a frictionless piston contains 10 L of air at ambient conditions, 100 kPa and 20oC. A force is now applied on the piston, compressing the gas until it reaches a set of stops, at which point the cylinder volume is 1 L. The insulation is now removed from the walls, and the gas cools down to the ambient temperature of 20oC. Calculate the (a) work and (b) heat transfer for the overall process. Also, show the process on a T-s diagram. Use the PG model. [Manual Solution*] [TEST Solution] 		Click on the image to animate!
Answers: (a) -3.78 kJ, (b) -3.78 kJ

A piston-cylinder device with a set of stops contains 12 kg of refrigerant-134a. Initially 9 kg of refrigerant is in the liquid form, and the temperature is -12oC. Now heat is transferred from the atmosphere at 25oC to the refrigerant until the piston hits the stop, at which point the volume is 380 L. Heating is continued until the temperature of the refrigerant reaches the atmospheric value. Determine (a) the final pressure, (b) the work transfer, (c) the heat transfer, and (d) the entropy generation during the entire process. [Manual Solution] [TEST Solution] 		Click on the image to animate!
Answers: (a) 654.2 kPa, (b) 9.68 kJ, (c) 1945.7 kJ, (d) 0.4366 kJ/K

A piston-cylinder device has a ring to limit the expansion stroke. Initially, the mass of air is 2 kg at 500 kPa, 30oC. Heat is now transferred until the piston touches the stop, at which point the volume is twice the original volume. More heat is transferred until the pressure inside also doubles. Using the IG model, determine (a) the amount of heat transfer, and (b) the final temperature. [Manual Solution] [Test Solution] 		 
Answers: (a) 1631 kJ, (b) 939.4oC  

An insulated container contains a block of ice of mass 1 ton (US) (1 US ton is 907.2 kg) at -20oC. The insulation is removed, and the ice gradually melts to water and comes to thermal equilibrium with the surroundings at 20°C. Assuming the pressure to remain constant at 100 kPa, determine the heat transfer during (a) the sensible heating of ice, (b) the melting of ice, and (c) the sensible heating of water. (c) What-if scenario: If the melting of ice in part (b) takes a period of 24 hours, what is the rate of heat transfer in kW? [Manual Solution*] [TEST Solution] 		Click on the image to animate!
Answers: (a) 36.81 MJ, (b) 302.48 MJ, (c) 76.19 MJ, (d) 3.5 kW

Three alternative processes shown in the accompanying figure are suggested to change the state of one kg of air from 0.8 MPa, 25°C (state-1) to 0.3 MPa, 60°C (state-5). Process 1-2-5 consists of a constant pressure expansion followed by a constant volume cooling, process 1-3-5 an isothermal expansion followed by a constant pressure expansion, and process 1-4-5 an adiabatic expansion followed by a constant volume heating. Determine the work and heat transfer for each alternative. [Manual Solution*] [Test Solution] 		Click on the image to animate!
Answers: (a) 194 kJ, 169 kJ, (b) 119 kJ, 94 kJ, (c) 101kJ, 76 kJ

Section-2: Closed Processes Involving Non-Uniform Mixing Systems
An insulated rigid tank is divided into two equal parts by a membrane. At the beginning, one part contains 3 kg of Nitrogen at 500 kPa and 50oC, and the other part is completely evacuated. The membrane is punctured and the gas expands into the entire tank. Determine the final (a) temperature and (b) pressure. Use the PG model. [Manual Solution] [TEST Solution] Click on the image to animate!
Answers: (a) 50oC, (b) 250 kPa

In the above problem, (a) determine the entropy generated during the expansion process. (b) What-if scenario: How would the answer change if the temperature of nitrogen was 100oC? [Manual Solution] [TEST Solution]
Answers: (a) 0.6175 kJ/K, (b) No change

A rigid, well insulated tank consists of two compartments, each having a volume of 1.5 m3, separated by a valve. Initially, one of the compartments is evacuated and the other contains nitrogen gas at 700 kPa and 100oC. The valve is opened and the nitrogen expands to fill the total volume, eventually achieving an equilibrium state. Determine the final (a) temperature and (b) pressure. Also determine (c) the entropy generated. Use the IG model. [Manual Solution] [TEST Solution]
Answers: (a) 100oC, (b) 350 kPa, (c) 1.95 kJ/K

An insulated cylinder is divided into two parts of 1 m3 each by a membrane. Side A has air at 200 kPa, 25oC, and side B has air at 1 MPa, 1000oC. The membrane is punctured so air comes to a uniform temperature. Determine (a) final pressure and temperature, (b) the entropy generated in this process. Use the PG model (c) What-if scenario: How would the answers change if the IG model was used? [Manual Solution] [TEST Solution]
Answers: (a) 600 kPa, 550oC, (b) 620 kPa, (b) 0.854 kJ/K, (c) 620 kPa, 579oC, 0.9195 kJ/K

A rigid tank has two compartments, one 500 times larger than the other. The smaller part contains 2 kg of compressed liquid water at 1 MPa and 25oC, while the other part is completely evacuated. The partition is now removed, and the water expands to fill the entire tank. Heat transfer with the atmosphere at 25oC is allowed, and, as a result, the final temperature after mixing is 25oC. Determine the final (a) pressure and (b) quality of the mixture. Also find (b) the entropy change of water, and (d) the entropy generation during the process. [Manual Solution*] [TEST Solution]
Answers: (a) 3.16 kPa, (b) 1.15%, (c) 0.1888 kJ/K, (d) 0.0106 kJ/K

An insulated rigid tank has two compartments, one 100 times larger than the other. The smaller part contains 2 kg of compressed liquid water at 400 kPa and 50oC, while the other part is completely evacuated. The partition is now removed, and the water expands to fill the entire tank. Determine (a) the final pressure, (b) temperature, (b) the entropy change of water, and (d) the entropy generation during the process. [Manual Solution*] [TEST Solution]
Answers: (a) 10.2 kPa, (b) 46.2 oC, (c) 0.0068 kJ/K, (c) 0.0068 kJ/K

A tank whose volume is unknown is divided into two parts by a partition. One side contains 0.02 m3 of saturated liquid R-12 at 0.7 MPa, while the other side is evacuated. The partition is now removed, and R-12 fills up the entire volume. If the final state is 200 kPa, 30o C. Determine (a) the volume of the tank, (b) the heat transfer. (c) What-if scenario: How would the answer in part (a) change if the final state was 300kPa and 30oC. [Manual Solution] [TEST Solution]
Answers: (a) 2.6 m3, (b) 3298.2 kJ, (c) 1.7 m 3

Four ice cubes (3 cm * 2 cm * 1 cm) at -15oC are added to an insulated glass of cola at 15oC. The volume of cola is 1.5 L. Determine (a) the equilibrium temperature, (b) and the total entropy change for this process. [Manual Solution*] [TEST Solution] 		Click on the image to animate!
Answers: (a) 13.5oC, (b) 0.0022 kJ/K

Two tanks are connected by a valve and line. The volumes are both 1 m3 with R-134a at 21o C, quality 25% in tank A and tank B ia evacuated. The valve is opened and saturated vapor flows from A to B until the pressure became equal. The process occurs slowly enough that all temperatures stay at 21oC during the process. Determine (a) the entropy generated, and (b) the total heat transfer. . [Manual Solution] [TEST Solution]
Answers: (a) 4719 kJ, (b) 2.22 kJ/K

A tank whose volume is unknown is divided into two parts by a partition. One side contains 0.02 m3 of saturated liquid R-12 at 0.7 MPa, while the other side is evacuated. The partition is now removed and R-12 fills up the entire volume. If the final state is 200 kPa, quality 90%, determine (a) the volume of the tank, (b) the heat transfer, and (c) the entropy generated. The atmospheric temperature is 30oC. (d) What-if scenario: How would the answer in part (b) change if the final pressure was 300 kPa? [Manual Solution] [TEST Solution] 		 
Answers: (a) 1.95 m3, (b) 2328.5 kJ, (c) 3 kJ/K, (d) 2466.6 kJ  

Two tanks are connected Part A tank is having 0.5 m3 containing hydrogen at 40oC, 200 kPa is connected to Part B tank having 1 m3 rigid tank containing hydrogen at 20oC, 600 kPa. The valve is opened and the system is allowed to reach thermal equilibrium with the surroundings at 15oC. Determine (a) the final pressure, (b) heat transfer, and (c) the entropy generated during the mixing process. Use the PG model. [Manual Solution] [TEST Solution] 		Click on the image to animate!
Answers: (a) 454.5 kPa, (b) -44.98 kJ, (c) 0.24 kJ/K

Two rigid tanks are connected by a valve. Tank A contains 0.4 m3 of water at 330 kPa and 90 percent quality. Tank B contains 0.5 m3 of water at 250 kPa and 250oC. The valve is now opened, and the two tanks eventually come to equilibrium while exchanging heat with the surroundings at 25oC. Determine (a) the final pressure, (b) heat transfer and (c) the entropy generation during the process. [Manual Solution] [TEST Solution]
Answers: (a) 3.15 kPa, (b) -3122.14 kJ, (c) 1.99 kJ/K

Two insulated tanks are connected, both containing H2O. Tank-A is at 200 kPa, v = 0.4 m3/kg, V = 1 m3 and tank B contains 3.5 kg at 0.5 MPa, 400oC. The valve is now opened and the two come to a uniform state. Find (a) the final pressure, (b) temperature and (c) the entropy generated by the mixing process. [Manual Solution*] [TEST Solution]
Answers: (a) 305.9 kPa, (b) 134.2oC, (c) 0.85 kJ/K

Two rigid tanks are connected by a valve as shown in the accompanying figure. Tank A is insulated and contains 0.1 m3 of steam at 500 kPa and 90% quality. Tank B is uninsulated and contains 2 kg of steam at 100 kPa and 300oC. The valve is now opened, and steam flows from tank A to tank B. As the pressure in tank A drops to 300 kPa, the valve is closed. During the process 500 kJ of heat is transferred from tank B to the surroundings at 25oC. Assuming the steam in tank A to have undergone a reversible adiabatic process (isentropic), determine (a) the final temperature in each tank, (b) final pressure in tank B, and (c) the entropy generated in the system's universe. [Manual Solution] [TEST Solution] 		Click on the image to animate!
Answers: (a) 133.6oC, 132.1oC (b) 74.1 kPa, (c) 0.7185 kJ/K

Two rigid tanks are connected by a valve. Tank A contains 1 m3 of air at 1 MPa, 200oC. Tank B contains 3 m3 of air at 100 kPa, 25oC. The valve is now opened, and air flows from tank A to tank B. Before the two gases comes to mechanical equilibrium, the valve is closed. After a sufficient time, air in both tanks comes to thermal equilibrium with the surroundings at 10 oC. The pressure in tank A is measured as 500 kPa. Using the PG model for air, determine (a) the final pressure in tank B, (b) the heat transfer, and (c) the entropy generated in the system's universe. [Manual Solution] [TEST Solution]
Answers: (a) 127.8 kPa, (b) -1040 kJ, (c) 1.39 kJ/K

An insulated tank containing 0.5 m3 of R-134a at 500 kPa and 90% quality is connected to an initially evacuated insulated piston-cylinder device as shown in the accompanying figure. The force balance on the piston is such that a pressure of 200 kPa is required to lift the piston. Now the valve is opened slightly and part of the refrigerant flows to the cylinder, pushing the piston up. The process ends when the pressure in the tank drops to 120 kPa. Assuming that the refrigerant in the tank undergoes an isentropic (reversible and adiabatic) process, determine the final quality in the (a) tank and (b) cylinder. Also calculate (c) the boundary work, and (d) the entropy generated during the process. [Manual Solution] [TEST Solution] 		Click on the image to animate!
Answers: (a) 0.898, (b) 0.974, (c) 188 kJ, (d) 0.6383 kJ/K

Section-3: Closed Process Involving Non-Uniform Non-Mixing Systems
A 40 kg aluminum block at 90oC is dropped into an insulated tank that contains 0.5 m3 of liquid water at 20oC. Determine the equilibrium temperature. [Manual Solution] [TEST Solution] Click on the image to animate!
Answer: 21.2oC

In the problem described above, determine the entropy generated during the process. [Manual Solution] [TEST Solution] 		 
Answer: 0.87 kJ/K  

A 25 kg aluminum block initially at 225oC is brought into contact with a 25 kg block of iron at 150oC in an insulating enclosure. Determine (a) the equilibrium temperature, (b) and the total entropy change for this process. [Manual Solution] [TEST Solution] 		Click on the image to animate!
Answer: (a) 200oC, (b) 0.097 kJ/K


A half kg bar of iron, initially at 782oC, is removed from an oven and quenched by immersing it in a closed tank containing 10 kg of water initially at 21oC. Heat transfer from the tank can be neglected. Determine (a) the equilibrium temperature, (b) and the total entropy change for this process. [Manual Solution] [TEST Solution]
Answer: (a) 25.08oC, (b) 0.29 kJ/K

A 15 kg block of copper at 100oC is dropped into an insulated tank that contains 1 m3 of liquid water at 20oC. Determine (a) the equilibrium temperature (b) the entropy generated in this process. [Manual Solution*] [TEST Solution]
Answer: (a) 20.11oC (b) .174 kJ/K

An unknown mass of iron at 80oC is dropped into an insulated tank that contains 0.1 m3 of liquid water at 20oC. Meanwhile, a paddle wheel driven by a 200 W motor is used to stir the water. When equilibrium is reached after 20 min, the final temperature is 25 oC. Determine (a) the mass of the iron block. (b) What-if scenario: How would the answer in part (a) change if the iron block was at 150 oC at the time of dropping. [Manual Solution] [TEST Solution] 		Click on the image to animate!
Answers: (a) 74.57 kg, (b) 31.81 kg

Section-4: Processes involving Open Systems

An insulated rigid tank is initially evacuated. A valve is opened and air at 100 kPa and 25oC enters the tank until the pressure in the tank reaches 100 kPa when the valve is closed. (a) Determine the final temperature of the air in the tank. Use the PG model. (b) What-if scenario: How would the answer change if the IG model was used? [Manual Solution*] [TEST Solution]
Answers: (a) 144.4°C, (b) 142.9oC

In the problem described above, determine the entropy generated during the process if the volume of the tank is 2 m3. [Manual Solution*] [TEST Solution]
Answers: 0.2821 kJ/K

A 3 m3 tank initially contains air at 100 kPa and 25oC. The tank is connected to a supply line at 550 kPa and 25oC. The valve is opened, and air is allowed to enter the tank until the pressure in the tank reaches the line pressure, at which point the valve is closed. A thermometer placed in the tank indicates that the air temperature at the final state is 65oC. Treating air as a perfect gas, determine (a) the mass of air that has entered the tank, (b) the heat transfer, and (c) the entropy generated. [Manual Solution*] [TEST Solution]
Answers: (a) 13.49 kg, (b) -665.4, (c) 2.7 kJ/K

An insulated rigid tank is initially evacuated. It is then connected through a valve to a supply line that carries steam at 2 MPa and 350oC. Now the valve is opened, and steam is allowed to flow slowly into the tank until the pressure reaches 2 Mpa, at which point the valve is closed. Determine the final temperature of the steam in the tank. [Manual Solution*] [TEST Solution]
Answers: 512oC

A completely evacuated, insulated, rigid tank with a volume of 8 m3 is filled from a steam line transporting steam at 450oC and 3.5 MPa. Determine (a) the temperature of steam in the tank when its pressure reaches 3.5 MPa. Also find (b) the mass of the steam that flows into the tank. [Manual Solution*] [TEST Solution]
Answers: (a) 630.2oC, (b) 68.14 kg

A 0.2 m3 tank initially contains R-12 at 1 MPa and x = 1. The tank is charged to 1.2 MPa, x = 0 from a supply line that carries R-12 at 1.5 MPa and 30oC. Determine (a) the final temperature and (b) the heat transfer. [Manual Solution*] [TEST Solution]
Answers: (a) 49oC, (b) 2803 kJ

In the charging process described above, determine (a) the change of entropy of refrigerant in the tank and (b) the entropy generation by the device and its surroundings. Assume the surrounding temperature to be 50oC. [Manual Solution*] [TEST Solution]
Answers: (a) 65.36 kJ/K, (b) 1.199 kJ/K

A 0.5 m3 rigid tank initially contains refrigerant-134a at 0.8 MPa and 100 percent quality. The tank is connected by a valve to a supply line that carries refrigerant-134a at 1.5 MPa and 30oC. Now the valve is opened, and the refrigerant is allowed to enter the tank. The valve is closed when it is observed that the tank contains saturated liquid at 1.5 MPa. Determine (a) the heat transfer. (b) mass of refrigerant that has entered the tank. [Manual Solution*] [TEST Solution]
Answers: (a) 16563 kJ, (b) 518.7 kg

An piston-cylinder device initially contains 0.1 m3 of steam at 200°C. The force on the piston is such that it maintains a constant pressure of 400 kPa inside. Due to heat rejection to the ambient air, the temperature of the steam drops down to 25°C. To restore the steam temperature to its original value, superheated steam from a supply line at 1 MPa, 600°C is introduced through a valve into the cylinder as shown in the accompanying figure. Neglecting any heat transfer during this charging process, determine (a) the heat transfer during the cooling process, and (b) the mass of steam introduced. [Manual Solution*] [TEST Solution]
Answers: (a) -515.8 kJ, (b) 0.453 kg

An insulated piston-cylinder device initially contains 0.01 m3 of steam at 200°C. The force on the piston is such that it maintains a constant pressure of 400 kPa inside. A valve is now opened and steam at 1 MPa, 200°C is allowed to enter the cylinder until the volume inside increases to 0.04 m3. Determine (a) the final temperature of the steam and (b) the amount of mass transfer. [Manual Solution*] [TEST Solution] 		 
Answers: (a) 189°C (b) 0.058 kg  

An insulated piston-cylinder device initially contains 0.2 m3 of R-134a, half (by volume) of which is in the vapor phase. The mass of the piston is such that it maintains a constant pressure of 200 kPa inside. A valve is now opened and all the liquid refrigerant is allowed to escape. Determine (a) the mass of liquid refrigerant in the beginning, (b) the mass withdrawn, and (b) the entropy generated during the process. [Manual Solution*] [TEST Solution]
Answers: (a) 132.5 kg, (b) 132.5 kg, (c) 0 kW/K

A 0.5 m3 tank initially contains saturated liquid water at 200oC. A valve in the bottom of the tank is opened and half the liquid is drained. Heat is transferred from a source at 300oC to maintain constant temperature inside the tank. Determine (a) the heat transfer. (b) What-if scenario: How would the answer in (a) change if the 0.5 m3 tank initially contained saturated liquid water at 100oC? [Manual Solution*] [TEST Solution]
Answers: (a) 3843 kJ, (b) 339 kJ

In the problem described above, determine the entropy generated in the system's universe during the discharge. [Manual Solution*] [TEST Solution]
Answers: 1.41 kJ/K

A 0.2 ft3 pressure cooker has an operating pressure of 40 psia. Initially 50% of the volume is filled with vapor and the rest with liquid water. Determine (a) the heat transfer necessary to vaporize all the water in the cooker. (b) What-if scenario: How would the answer change if initially 20% of the volume was filled with vapor? [Manual Solution*] [TEST Solution]
Answers: (a) 5445 Btu, (b) 8713 Btu

 

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