One kilogram of nitrogen gas (N2) is undergoes an isothermal compression from 1

Question

One kilogram of nitrogen gas (N2) is undergoes an isothermal compression from 1 bar, 20C to a final pressure of 12 bar. During the process, the nitrogen transfers heat through a wall to a thermal reservoir with a temperature of 10C.

a) For the nitrogen gas as the system, evaluate the work and heat transfer for this process and determine the amount of entropy producation, kJ/K.

b) For an expanded system that includes the wall, calcualte the work, heat transfer and entropy producation. Why do the results differ?

Explanation / Answer

Work done in isothermal process w = mRT ln (P1 / P2)

= 1*(8.314/28)*(20+273) ln (1/12)

= -216.18 kJ

Heat transfer q = w + (u2 u1)

But u2 u1 = 0 since isothermal process

So, heat transfer q = w = -216.18 kJ

Entropy production ds = Q/T

= -216.18 / (20+273)

= -0.7378 kJ/K

b)

Work done on the control volume consisting (wall + gas) will be +216.18 kJ.

Heat transfer on the control volume consisting (wall + gas) will be + 216.18 kJ.

Entropy change of atmosphere = 216.18 / (10+273) = 0.7639 kJ/K

Net entropy change = 0.7639 0.7378 = 0.026 kJ/K

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