Question

A quantity of heat $Q$ is supplied to a monoatomic ideal gas which expands at constant pressure. The fraction of heat that goes into work done by the gas $\left(\frac{W}{Q}\right)$ is

• A. $\frac{2}{5}$
• B. $\frac{3}{5}$
• C. $\frac{2}{3}$
• D. 1

Answer 1

Answer: (A)

Take 1 mole of gas $C_{p} \Delta T=C_{v} \Delta T+\Delta W$
$\therefore \Delta W=\left(C_{p}-C_{v}\right) \Delta T$
Fraction of heat converted into work
$\frac{\Delta W}{\Delta Q}=\frac{\left(C_{p}-C_{v}\right) \Delta T}{C_{p} \Delta T}$
$=-1-\frac{1}{\gamma} =\left(1-\frac{3}{5}\right)=\frac{2}{5}$