Question

A gas is expanded to double its volume by two different processes. One is isobaric and the other is isothermal. Let $W_{1}$ and $W_{2}$ be the respective work done, then :

• A. $W_{2}=W_{1} \ln (2)$
• B. $W_{2}=\frac{W_{1}}{\ln (2)}$
• C. $W_{2}=\frac{W_{1}}{2}$
• D. Data is insufficient

Answer 1

Answer: (A)

In isobaric process,
$W_{1}=p(2 V-V)=p V$
In isothermal process .
$W_{2}=n R T \ln \left(\frac{2 V}{V}\right)=n R T \ln (2)$
$\Rightarrow W_{2} =p V \ln (2)$
$\Rightarrow \frac{W_{1}}{W_{2}} =\frac{p V}{p V \ln (2)}=\frac{1}{\ln (2)}$
$\Rightarrow W_{2} =W_{1} \ln (2)$