Question

A sample of an ideal gas with initial pressure P and volume V is taken through an isothermal process during which entropy change is found to be $\Delta$S. The universal gas constant is R. Then, the work done by the gas is given by:

• A. $\frac{PV\Delta S}{nR}$
• B. $nR\Delta S$
• C. PV
• D. $\frac{P\Delta S}{nRT}$

Answer 1

Answer: (A)

$\frac{PV\Delta S}{nR}$

Dimensional analysis,

work done $=$ Energy $=\frac{PV△S}{nR}$

We know, $PV=nRT.$

$⟹Energy=\frac{PVT△S}{nRT}=T△S,$

Also, $△S=\frac{△H}{T}$

Energy $=\frac{△H}{T}\times T$

Energy $=$ Energy.

$\therefore R.H.S=L.H.S⟹$ Work done by gas is $\frac{PV△S}{nR}.$