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An ideal gas is expanding such that $\mathrm{PT}^{3}=$ constant. The coefficient of volume expansion of the gas is:

Option: 1 $\frac{2}{T}$
Option: 2 $\frac{3}{T}$
Option: 3 $\frac{1}{T}$
Option: 4 $\frac{4}{T}$

Answers (1)

best_answer

$PT^{3}\doteq K\cdots \left ( Given \right )$
$For \: Ideal\: gas , PV= nRT$
$\left ( \frac{T}{V} \right )T^{3}= constant$
$V^{-1}T^{4}= constant$
$VT^{-4}= constant$
$V\left ( -4T^{-5} \right )+T^{-4} \frac{dV}{dT}= 0$
$-4VT^{-5}= -T^{-4}\frac{dV}{dT}$
$4T^{-1}= \frac{dV}{VdT}$
$\gamma = \frac{dV}{VdT}= coefficent\, of\, volume\, expansion$
$\gamma = \frac{4}{T}$
The correct option is (4) .

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vishal kumar

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