ned in a cylinder and undergoes an isothermal expansion according to the law p = A + Bv, where p is the pressure in bar, v is the volume in m' and A and B are constants. The initial and final pressures are 8.4 bar and 2.8 bar and the corresponding volumes are 0.056 m' and 0.168 m'. Find 1. workdone by the gas, 2. heat transferred during the process, and 3. change in entropy per kg of gas during expansion. Take R = 275 J/kg K. Ans. 62.72 kJ: 62 72 kJ:03018 kJ/kg Kl 9. Calculate the change of entropy when 0.14 kg of gas initially at 170 C expands with a volume ratio of 5.4 according to pol 24 Constant. Take y= 1.4 and R=287 kJ/kg K. [Ans. 0.027 kJ/K] 0. One kg of air at a pressure of 7 bar and a temperature of 363 K undergoes a reversible polytropic process which may be represented by pul Constant. The final pressure is 1.4 bar. Evaluate: 1. The final specific volume, temperature and increase in entropy; and 2. The workdone and heat transfer during the process. Assume R = 287 J/kg K and y= 1.4. [Ans. 0.643 m², 313.3 K, 0.316 kJ/K: 142 64 kJ. 107.04 kJ 1. One kg of air at 1 bar and 15" C is compressed according to pol 25= Constant to a pressure of 16 bar. Calculate the temperature at the end of compression, the heat received or rejected by the air during the process and the change of entropy. Sketch the operation on temperature-entropy diagram. Take c = 1.005 kJ/kg K, c, = 0.716 kJ/kg K. [Ans. 228.7° C: 92.6 kJ (rejected): 0.238 kJ/K (decrease)] 2. An ideal gas of molecular mass 30 and specific heat ratio 1.38 is compressed according to the law pol 25 = Constant, from a pressure of 1 bar and 15° C to a pressure of 16 bar. Calculate the temperature at the end of compression, the heat received or rejected and workdone by the gas during the process and the change in entropy. Assume 1 kg mass of the gas. Use only calculated values of Cp and C [Ans. 228.7° C; 81 kJ (rejected): 0.21 kJ/K (decrease)] 13. A gas engine mixture at 95° C and 1 bar is compressed with index of compression 1.3, the volume compression ratio being 6: 1. The maximum pressure is 25 bar. Assuming the ratio of specific heats as 1.38 and the specific heat at constant volume as 0.754 kJ/kg K, find the change in entropy during compression stroke and during combustion which takes place at constant volume. Represent the process on p-v and T-s planes. [Ans. 0.108 kJ/K (decrease); 0.67 kJ/K] 14. An ideal gas at temperature T, is heated at constant pressure to T₂ and then expanded reversibly according to the law pu" = Constant, until the temperature is again T₁. Find the value of n, if the changes in 27 entropy during the separate processes are equal. Ans. 15. The work done by 0.07 kg of air when it expands according to po = Constant is 7.6 kJ. The temperature of air falls from an initial value of 105° C to a final value of 13° C during the process. Determine : 1. the heat supplied or rejected by the air during the expansion; 2. the value of index n; and 3. the change of entropy, stating whether this is an increase or decrease. y = 1.4 and c, = 0.712 kJ/kg K. [Ans. 3 kJ: 1.24; 0.009 26 kJ/K (increase)] 1. One kg of air at 1 bar and 27" C is compressed isothermally to one-fifth the original volume. It is then heated at constant volume to a condition such that isentropic expansion from that state will return the systen. to the original state. Determine the pressure and temperature at the end of constant volume heating. Represent the processes on pressure-volume and temperature-entropy diagrams, and find: 1. the change in entropy during each process; and 2. net workdone during the cycle. [Ans. 9.518 bar, 571.08 K: -0.46 kJ/K, 0.46 kJ/K, zero ; 56.08 kJ] 17. 0.056 m² of carbon monoxide is contained in a cylinder at 37" C and 1.4 bar. The gas is compressed to 0.0224 m³ during the inward stroke of the piston. If the compression process is (a) isothermal, and (b) adiabatic, find: 1. final temperature and pressure, 2. workdone, and 3. change of entropy. Take c, = 1.047 kJ/kg K and C = 0.749 kJ/kg K. [Ans. 310 K, 3.5 bar, -7.176 kJ, -0.0232 kJ/K; 447.2 K, 5.05 bar, -8.68 kJ, zero]

ned in a cylinder and undergoes an isothermal expansion according to the law p = A + Bv, where p is the pressure in bar, v is the volume in m' and A and B are constants. The initial and final pressures are 8.4 bar and 2.8 bar and the corresponding volumes are 0.056 m' and 0.168 m'. Find 1. workdone by the gas, 2. heat transferred during the process, and 3. change in entropy per kg of gas during expansion. Take R = 275 J/kg K. Ans. 62.72 kJ: 62 72 kJ:03018 kJ/kg Kl 9. Calculate the change of entropy when 0.14 kg of gas initially at 170 C expands with a volume ratio of 5.4 according to pol 24 Constant. Take y= 1.4 and R=287 kJ/kg K. [Ans. 0.027 kJ/K] 0. One kg of air at a pressure of 7 bar and a temperature of 363 K undergoes a reversible polytropic process which may be represented by pul Constant. The final pressure is 1.4 bar. Evaluate: 1. The final specific volume, temperature and increase in entropy; and 2. The workdone and heat transfer during the process. Assume R = 287 J/kg K and y= 1.4. [Ans. 0.643 m², 313.3 K, 0.316 kJ/K: 142 64 kJ. 107.04 kJ 1. One kg of air at 1 bar and 15" C is compressed according to pol 25= Constant to a pressure of 16 bar. Calculate the temperature at the end of compression, the heat received or rejected by the air during the process and the change of entropy. Sketch the operation on temperature-entropy diagram. Take c = 1.005 kJ/kg K, c, = 0.716 kJ/kg K. [Ans. 228.7° C: 92.6 kJ (rejected): 0.238 kJ/K (decrease)] 2. An ideal gas of molecular mass 30 and specific heat ratio 1.38 is compressed according to the law pol 25 = Constant, from a pressure of 1 bar and 15° C to a pressure of 16 bar. Calculate the temperature at the end of compression, the heat received or rejected and workdone by the gas during the process and the change in entropy. Assume 1 kg mass of the gas. Use only calculated values of Cp and C [Ans. 228.7° C; 81 kJ (rejected): 0.21 kJ/K (decrease)] 13. A gas engine mixture at 95° C and 1 bar is compressed with index of compression 1.3, the volume compression ratio being 6: 1. The maximum pressure is 25 bar. Assuming the ratio of specific heats as 1.38 and the specific heat at constant volume as 0.754 kJ/kg K, find the change in entropy during compression stroke and during combustion which takes place at constant volume. Represent the process on p-v and T-s planes. [Ans. 0.108 kJ/K (decrease); 0.67 kJ/K] 14. An ideal gas at temperature T, is heated at constant pressure to T₂ and then expanded reversibly according to the law pu" = Constant, until the temperature is again T₁. Find the value of n, if the changes in 27 entropy during the separate processes are equal. Ans. 15. The work done by 0.07 kg of air when it expands according to po = Constant is 7.6 kJ. The temperature of air falls from an initial value of 105° C to a final value of 13° C during the process. Determine : 1. the heat supplied or rejected by the air during the expansion; 2. the value of index n; and 3. the change of entropy, stating whether this is an increase or decrease. y = 1.4 and c, = 0.712 kJ/kg K. [Ans. 3 kJ: 1.24; 0.009 26 kJ/K (increase)] 1. One kg of air at 1 bar and 27" C is compressed isothermally to one-fifth the original volume. It is then heated at constant volume to a condition such that isentropic expansion from that state will return the systen. to the original state. Determine the pressure and temperature at the end of constant volume heating. Represent the processes on pressure-volume and temperature-entropy diagrams, and find: 1. the change in entropy during each process; and 2. net workdone during the cycle. [Ans. 9.518 bar, 571.08 K: -0.46 kJ/K, 0.46 kJ/K, zero ; 56.08 kJ] 17. 0.056 m² of carbon monoxide is contained in a cylinder at 37" C and 1.4 bar. The gas is compressed to 0.0224 m³ during the inward stroke of the piston. If the compression process is (a) isothermal, and (b) adiabatic, find: 1. final temperature and pressure, 2. workdone, and 3. change of entropy. Take c, = 1.047 kJ/kg K and C = 0.749 kJ/kg K. [Ans. 310 K, 3.5 bar, -7.176 kJ, -0.0232 kJ/K; 447.2 K, 5.05 bar, -8.68 kJ, zero]

Refrigeration and Air Conditioning Technology (MindTap Course List)

8th Edition

ISBN:9781305578296

Author:John Tomczyk, Eugene Silberstein, Bill Whitman, Bill Johnson

Publisher:John Tomczyk, Eugene Silberstein, Bill Whitman, Bill Johnson

Chapter1: Heat, Temperature, And Pressure

Section: Chapter Questions

Problem 6RQ: One British thermal unit will raise the temperature of _____ 1b of water _____F.

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