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  4. When heat Q is supplied to a diatomic gas of rigid molecules, at constant volume its temperature increases by Δ T. The heat required to produce the same change in temperature, at a constant pressure is :

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Q. When heat $Q$ is supplied to a diatomic gas of rigid molecules, at constant volume its temperature increases by $\Delta T$. The heat required to produce the same change in temperature, at a constant pressure is :

JEE MainJEE Main 2019Kinetic Theory

Solution:

$Q = nC_{v} \Delta T $
$ Q' =nC_{p} \Delta T $
$ \therefore \frac{Q'}{Q} = \frac{C_{p}}{C_{v}} $
For diatomic gas : $ \frac{C_{p}}{C_{v}} =\gamma = \frac{7}{5} $
$ Q' = \frac{7}{5} Q $