A sample of dry air has an initial pressure p1 = 1000hPa and temperature T1 = 30

Question

A sample of dry air has an initial pressure p1 = 1000hPa and temperature T1 = 300K. It undergoes a process that takes it to a new pressure p2 = 500hPa with unchanged temperature T2 = T1. Compute the mechanical work per unit mass performed by the sample under the following scenarios:

a) Isochoric pressure reduction to p2 followed by isochoric expansion to final state.

b) Isobaric expansion to final specific volume v2 followed by isochoric pressure reduction to final state.

c) Isothermal expansion to final state.

Explanation / Answer

P1V1 = nRT1 P2V2 = nRT2 taking 1 kg of air n=1/28.9 R=8.31 we get V1=8.626*10^-4 m3/kg V2=2V1 a) The work is done only when there is change in volume. W=P2(V2-V1) = 43.13J b) W=P1(V2-V1) =86.26J c) nRT ln(V2/V1) =59.79J

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