A certain fixed mass system involving an ideal gas undergoes a polytropic proces

Question

A certain fixed mass system involving an ideal gas undergoes a polytropic process. The following are given.

a) Q(1->2)= +2966.253179KJ (Heat transfer to the system during the process.
b) Polytropic exponent n=1.0
c) V2=9m^3 (final volume, state 2)
d) V1=3m^3 (initial volume, state 1)

Determine:

1) (u2-u1) (Change in specific internal energy)
2) W(1->2) (Work done on or by the system)
3) P2 (The final pressure, state2)

Explanation / Answer

a) Q(1->2) = +2966.253179 kJ b) Polytropic exponent n = 1.0, so it is actually a isothermal process c) V2 = 9 m^3 (final volume, state 2) d) V1 = 3 m^3 (initial volume, state 1) 1) (u2 - u1) = 0 2) W(1->2) = Q(1->2) = +2966.253179 kJ 3) P2 (The final pressure, state2) Q = P2*V2*ln(V2/V1) = P2*9*ln(9/3) so P2 = 300 kPa

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