(a) Explanation Write the ideal gas equation to calculate the mass of the gas ( m ) . m = P 1 V 1 R T 1 (I) Here, initial pressure of the gas is P 1 , initial volume of the gas is V 1 , gas constant is R , and the initial temperature is T 1 . Write the energy balance equation for the entire system considering it as a stationary closed system. E in − E out = Δ E system ︸ = 0 0 = Δ U 0 = [ m c v ( T 2 − T 1 ) ] N 2 + [ m c v ( T 2 − T 1 ) ] He (II) Here, net energy input to the system is E in , net energy output to the system is E out , the change in net energy is Δ E system , change in internal energy is Δ U , constant volume specific heat is c v , final temperature is T 2 , and the initial temperature is T 1 . Conclusion: Refer the Table A-1E of “Molar mass, gas constant, and critical-point properties”, obtain the gas constants of Nitrogen and Helium as R N 2 = 0.2968 kPa ⋅ m 3 / kg ⋅ K R He = 2.0769 kPa ⋅ m 3 / kg ⋅ K Refer the Table A-2E of “Ideal-gas specific heats of various common gases”, obtain the specific heats of Nitrogen and Helium as c p , N 2 = 1.039 kJ / kg ° C c v , N 2 = 0.743 kJ / kg ° C c p , He = 5.1926 kJ / kg ° C c v , He = 3.1156 kJ / kg ° C Substitute 500 kPa for P 1 , 1 m 3 for V 1 , 0.2968 kPa ⋅ m 3 / kg ⋅ K for R N 2 , and 353 K for T 1 , N 2 in Equation (I) (b) To determine The amount of wasted work potential for the process. The amount of wasted work potential for the process when piston is restricted from moving.

8th Edition

ISBN: 9780073398174

Author: Yunus A. Cengel Dr., Michael A. Boles

Publisher: McGraw-Hill Education

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Chapter 8.8, Problem 106RP

(a)

To determine

The final temperature in the cylinder at equilibrium condition.

(b)

To determine

The amount of wasted work potential for the process.

The amount of wasted work potential for the process when piston is restricted from moving.

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Chapter 8.8, Problem 105RP

Chapter 8.8, Problem 107RP

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Argon gas is contained in a cylinder fitted with a frictionless piston. Initially, the cylinder contains 200 L of Argon at 140 kPa and 10o C. The gas is then compressed in a polytropic process according to the relationship Pvn = C until the final pressure and temperature are 700 kPa and 180o C respectively. For Argon; R = 0.2081 kJ/kg.K and cv = 0.3122 kJ/kg.K. i) Sketch the system and the details of the process. ii) Show the process on a P-v diagram iii) Determine the polytropic exponent, n iv) Calculate the work involved during the process [kJ] v) Calculate the heat transfer during this process [kJ]

Consider a well-insulated horizontal rigid cylinder that is divided into two compartments by a piston that is free to move but does not allow either gas to leak into the other side. Initially, one side of the piston contains 1 m3 of N2 gas at 500 kPa and 80°C while the other side contains 1 m3 of He gas at 500 kPa and 25°C. Now thermal equilibrium is established in the cylinder as a result of heat transfer through the piston. Using constant specific heats at room temperature, determine the wasted work potential during this process. What would your answer be if the piston were not free to move? Take T0 = 25°C.

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The final temperature in the cylinder at equilibrium condition.

Solution Summary: The author analyzes the energy balance equation for the entire system considering it as a stationary closed system.

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The final temperature in the cylinder at equilibrium condition.

The amount of wasted work potential for the process. The amount of wasted work potential for the process when piston is restricted from moving.

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The amount of wasted work potential for the process.

The amount of wasted work potential for the process when piston is restricted from moving.