Question

a reversible non-flow process with a gas is defined by the equation pv=c. show that the work done is given by the equation wk12=p1v1ln(V2/V1)

Answer 1

Work done in a thermodynamic process is given by $\int pdV$

$pV=c\\p=c/V$

substituting this into the work done formula we get

Work done = $\smallint \frac{c}{V}dV$

Integrating this with limits $V_1$ to $V_2$

Work done =$[c\ln V]^{V_2}_{V_1}$ =$c\ln\frac{V_2}{V_1}$

as we are given pV=c which means p₁V₁=c

substituting the value of c , we get

Work done = $p_1V_1\ln{\frac{V_2}{V_1}}$