Question

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

• A. $\frac{3}{T}$
• B. $\frac{4}{T}$
• C. $\frac{1}{T}$
• D. $\frac{2}{T}$

Answer 1

The correct option is B $\frac{4}{T}$

Given :-
$P{T}^3=k$ (let)
$\Rightarrow \left(\frac{nRT}{V}\right)\times T^3=k$
Or, $\frac{T^4}{V}=k^{\prime }$
Differentiating the equation :-
$\frac{4T^3}{V}dT-\frac{T^4}{V^2}dV=0$
$\Rightarrow \frac{dV}{VdT}=\frac{4}{T}$
$\Rightarrow \beta =\frac{4}{T}$
Where, $\beta =\frac{dV}{VdT}$ is the coefficient of volume expansion.