Ten moles of a diatomic perfect gas are allowed to expand at constant pressure. The initial volume and temperature are $V_{0}$ and $T_{0}$ respectively. If $\frac{7}{2} R T_{0}$ heat is transferred to the gas then the final volume and temperature are

1.1 V_{0}, 1.1 T_{0}

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0.9 V_{0}, 0.9 T_{0}

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1.1 V_{0}, \frac{10}{11} T_{0}

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0.9 V_{0}, \frac{10}{9} T_{0}

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Solution

The correct option is A $1.1 V_{0}, 1.1 T_{0}$
Given : $n = 10 C_{p} = \frac{7}{2} R$ (diatomic gas)
$Q_{p} = n C_{p} Δ T$
$\frac{7}{2} R T_{o} = 10 \times \frac{7}{2} R (T - T_{o})$
$⟹ T = 1.1 T_{o}$
Also as P is constant, $⟹ V \propto T$
Thus $\frac{V}{V_{o}} = \frac{1.1 T_{o}}{T_{o}}$
$⟹ V = 1.1 V_{o}$

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