Question:
An ideal gas is expanding such that $\mathrm{PT}^{3}=$ constant. The coefficient of volume expansion of the gas is:
Correct Option: , 3
Solution:
$\mathrm{PT}^{3}=\mathrm{constant}$
$\left(\frac{\mathrm{nRT}}{\mathrm{V}}\right) \mathrm{T}^{3}=\mathrm{constant}$
$\mathrm{T}^{4} \mathrm{~V}^{-1}=\mathrm{constant}$
$\mathrm{T}^{4}=\mathrm{kV}$
$\Rightarrow 4 \frac{\Delta \mathrm{T}}{\mathrm{T}}=\frac{\Delta \mathrm{V}}{\mathrm{V}}$...(1)
$\Delta \mathrm{V}=\mathrm{V} \gamma \Delta \mathrm{T}$...(2)
comparing (1) and (2)
we get
$\gamma=\frac{4}{\mathrm{~T}}$
Click here to get exam-ready with eSaral
For making your preparation journey smoother of JEE, NEET and Class 8 to 10, grab our app now.