An ideal gas is expanding


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

  1. $\frac{1}{T}$

  2. $\frac{2}{\mathrm{~T}}$

  3. $\frac{4}{T}$

  4. $\frac{3}{\mathrm{~T}}$

Correct Option: , 3



$\left(\frac{\mathrm{nRT}}{\mathrm{V}}\right) \mathrm{T}^{3}=\mathrm{constant}$

$\mathrm{T}^{4} \mathrm{~V}^{-1}=\mathrm{constant}$


$\Rightarrow 4 \frac{\Delta \mathrm{T}}{\mathrm{T}}=\frac{\Delta \mathrm{V}}{\mathrm{V}}$...(1)

$\Delta \mathrm{V}=\mathrm{V} \gamma \Delta \mathrm{T}$...(2)

comparing (1) and (2)

we get


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