Question

An ideal gas is expanding such that $P{T}^2=\text{constant}$. The coefficient of volumetric expansion of the gas is

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

Answer 1

The correct option is C $\frac{3}{T}$

From ideal gas equation $PV=nRT\Rightarrow P=\frac{nRT}{V}$

Given
$P{T}^2=K\frac{nRT}{V}.T^2=KnR{T}^3=KV\dots \dots \left(i\right)$
Differentiating both sides, we get $3nR{T}^{2}dT=KdV\dots \dots \left(ii\right)$
Dividing equation (ii) by (i) we get $\frac{3}{T}dT=\frac{dV}{V}$
Coefficient of volume expansion $=\frac{dV}{VdT}=\frac{3}{T}$