4. A gas contained within a piston-cylinder assembly undergoes two processes, A

Question

4. A gas contained within a piston-cylinder assembly undergoes two processes, A and B, between the same end states, 1 and 2, where p 1 =10 bar, V 1= 0.1 m^3, U1 = 400 kJ and p 2 = 1 bar, V2 = 1.0 m^3, U2 :200 kj: Process A: Process from 1 to 2 during which the pressure-volume relation is pV = constant. Process B: Constant-volume process from state 1 to a pressure of 2 bar, followed by a linear pressure-volume process to state 2. Kinetic and potential energy effects can be ignored. For each of the processes A and B, (a) sketch the process on p - V coordinates, (b) evaluate the work, in kJ, and (c) evaluate the heat transfer, in kJ.

Explanation / Answer

Only the change of internal energy is the same. It does not depend on the path. Work and heat transfer do depend on the path.
Work is given by the integral
W = - ? p dV along the path
If you choose a different path. i.e. a different relation between p and V the work change. Q on this path changes too, giving overall the same change of internal energy:
?U = Q + W

The change of internal energy is the same in both cases
?U_A = ?U_B = U? - U? = 200kJ - 400kJ = -200kJ

For process A
p?V = constant = p??V?
hence:
p = p??V? / V
and
W_A = - p??V?? ? 1/V dV from V? to V?
= - p??V?? ln(V?/V?)
= - 10^6Pa ? 0.1m

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