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Question:
1 mole of rigid diatomic gas performs a work of $\mathrm{Q} / 5$ when heat $\mathrm{Q}$ is supplied to it. The molar heat capacity of the gas during this
transformation is $\frac{x R}{8}$, The value of $x$ is
$[\mathrm{K}=$ universal gas constant $]$
Solution:
$\mathrm{Q}=\Delta \mathrm{U}+\mathrm{W}$
$\mathrm{Q}=\Delta \mathrm{U}+\frac{\mathrm{Q}}{5}$
$\Delta U=\frac{4 Q}{5}$
$\mathrm{nC}_{\mathrm{v}} \Delta \mathrm{T}=\frac{4}{5} \mathrm{nC} \Delta \mathrm{T}$
$\frac{5}{4} C_{V}=C$
$\mathrm{C}=\frac{5}{4}\left(\frac{\mathrm{f}}{2}\right) \mathrm{R}=\frac{5}{4}\left(\frac{5}{2}\right) \mathrm{R}$
$C=\frac{25}{8} R$
$x=25$
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