Question

Derive the Expression for manimum work done in an adiabatic expansion of an usual gas​

Answer 1

Answer:

Adiabatic process : PV

γ

=K

So, P=KV

−γ

Work done W=∫PdV

Or W=∫KV

−γ

dV

Or W=K×

1−γ

V

−γ+1

∣

∣

∣

∣

∣

V

1

V

2

Or W=

1−γ

K

×[V

2

−γ+1

−V

1

−γ+1

]

Or W=

1−γ

1

×[KV

2

−γ+1

−KV

1

−γ+1

]

Or W=

1−γ

1

×[P

2

V

2

γ

V

2

−γ+1

−P

1

V

1

γ

V

1

−γ+1

]

Or W=

1−γ

P

2

V

2

−P

1

V

1