Air in an insulated piston cylinder is initially at 400K and 100 kPa. The air is

Question

Air in an insulated piston cylinder is initially at 400K and 100 kPa. The air is compressed isentropically until the pressure is 200 kPa. How much work (kJ/kg) is required for the compression? Use the PG model (constant specific heat) to calculate the answer.   

Air in an insulated piston cylinder is initially at 400K and 100 kPa. The air is compressed isentropically until the pressure is 200 kPa. How much work (kJ/kg) is required for the compression? Use the PG model (constant specific heat) to calculate the answer.   

[None Given]

Explanation / Answer

The process given is Isentropic that means it is a constant adiabatic process.

dQ = 0

W isen =(P1V1 - P2V2)/ Y-1

P1V1^Y. =P2V2^Y

100/200=(V2/V1)^1.4

0.5^1/1.4= V2/V1

0.609 = V2/V1

W= (100-200*.609)/1.4-1

= -54.5Kj/Kg.

Negative sign because of compression,I.e. work is done on the Piston and not by the Piston.

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