Question

One mole of an ideal monoatomic gas undergoes a process as shown in the figure. Find the molar specific heat of the gas in the process ($R$ is a gas constant).

• A. $\frac{3R}{4}$
• B. $\frac{R}{2}$
• C. $\frac{R}{3}$
• D. $\frac{2R}{3}$

Answer 1

The correct option is B $\frac{R}{2}$

$V=m\left(\frac{1}{T}\right);m=\mathrm{slope}\mathrm{of}\mathrm{the}\mathrm{curve}VT=\mathrm{Constant};TdV+VdT=0dV=-\frac{V}{T}dT\left(1\right)Q=\Delta U+WCdT=C_{v}dT+PdV$
From equation $\left(1\right)$
$CdT=C_{v}dT-\frac{P}{T}VdT\Rightarrow C=C_v-\frac{PV}{T}\mathrm{For}\mathrm{monoatomic}\mathrm{gas}{C}_v=\frac{3}{2}RC=C_v-R=\frac{3}{2}R-R\Rightarrow C=\frac{R}{2}$