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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

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$1.1 V_{0}, 1.1 T_{0}$

$0.9 V_{0}, 0.9 T_{0}$

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

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

answer is A.

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Detailed Solution

$∵ Q = n C_{p} Δ T$

$\frac{7}{2} R T_{0} = (10) (\frac{7}{2} R) (T_{f} - T_{0})$

$T_{f} = 1.1 T_{0}$

$If p = constant, then V \propto T$

If temperature becomes $1.1$ times, then volume will also becomes $1.1$ times

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