A gas is found to obey the law $P^{2} V = c o n s t a n t$ . The initial temperature and colume are $T_{0} a n d V_{0}$ . If the gas expands to a volume $3 V_{0}$ , then the final temperature becomes

\sqrt{3} T_{0}

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\sqrt{2} T_{0}

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\frac{T_{0}}{\sqrt{3}}

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\frac{T_{0}}{\sqrt{2}}

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Solution

The correct option is C $\sqrt{3} T_{0}$
It is given that $P^{2} V = c o n s t a n t = k$ (let)
From Ideal Gas Law, $P V = n R T$
$⟹ P = \frac{n R T}{V}$
$⟹ (\frac{n R T}{V})^{2} V = k$
$⟹ \frac{T^{2}}{V} = k^{'}$
$⟹ (\frac{T^{'}}{T_{0}})^{2} = \frac{V^{'}}{V_{0}}$
$⟹ T^{'} = \sqrt{3} T_{0}$

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