1 mole of rigid diatomic gas performs a work

Question:

1 mole of rigid diatomic gas performs a work of $\frac{Q}{5}$ when heat $Q$ is supplied to it. The molar heat capacity of the gas during this transformation is $\frac{x R}{8}$. The value of $x$ is

Solution:

(25)

From thermodynamics law:

$\Delta \mathrm{Q}=\Delta \mathrm{U}+\Delta \mathrm{W} \quad \ldots . .(1)$

$\mathrm{Q}=\mathrm{n} \mathrm{C}_{\mathrm{v}} \Delta \mathrm{T}+\frac{Q}{5}$

$Q-\frac{Q}{5}=1 \times \frac{5}{2} R \times \Delta \mathrm{T}$

$\mathrm{Q}=\frac{25}{8} R \Delta \mathrm{T} \quad \ldots \ldots(2) \quad \therefore \mathrm{Q}=\mathrm{nc} \Delta \mathrm{T}$

$c=\frac{25}{8} R \quad$ given $C=\frac{x R}{8}$

$x=25$