An ideal gas is expanding such that $P T^{2} = c o n s t a n t$ . The coefficient volume expansion of the gas is

\frac{1}{T}

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\frac{2}{T}

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\frac{3}{T}

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\frac{4}{T}

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Solution

The correct option is C $\frac{3}{T}$
We know, $γ = \frac{1}{v} \frac{d v}{d T}$
Given, $P T^{2} = c o n s t a n t = k (s a y)$
To find $\frac{d v}{d T}$ we need to express V in terms of T
From ideal gas equation, PV = nRT
$\Rightarrow \frac{k v}{T^{2}} = n R T \Rightarrow V = \frac{n R}{k} T^{3} \frac{d v}{d T} = \frac{n R}{k} (3 T^{2}) γ = \frac{1}{(\frac{n R}{k} T^{3})} \times (\frac{n R}{k} 3 T^{2}) = \frac{3}{T}$

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