Question

An ideal gas has adiabatic exponent gamma. It expands according to the law

Answer 1

Law of the process is p = αV or pV-1 =α

so the process is polytropic of index n = -1

AS p= αV so, pi = αV0 and pf = αηV0

Therefore to improve the internal energy, it is given by

Δv=vR/γ-1 [Tf-Ti] = pfVf-piVi/γ-1

Moreover, the work performed by the gas

A=piVi-pfVf/n-1 = αV0²-αηV0.ηV0/-1-1

=αV0² (1-n²)/-2

=1/2 αV0²(η²-1)

The capacity of the heat is given by

Cn = R(n-γ)/(n-1)(γ-1)

= R(n-γ)/(-1-1)(γ-1)

= R/2 γ+1/γ-1