Question

Two moles of a gas is expanded to double its volume by two different processes. One is isobaric and the other is isothermal. If $w_1$ and $w_2$ are the works done respectively, then

• A. $w_2=\frac{w_1}{ln2}$
• B. $w_2=w_1$
• C. $w_2=w_{1}ln2$
• D. $w_1^2=w_{2}ln2$

Answer 1

The correct option is C $w_2=w_{1}ln2$

In isobaric process volume is proportional to the temprature, so work done is $w_1=P(2V-V)=PV=nRT$.
work done in isothermal process is $w_2=nRTln\left(\frac{2V}{V}\right)=nRTln\left(2\right)$
thus, $w_2=w_{1}ln\left(2\right)$