Question

Calculate total heat capacity of 40 g triatomic nonlinear gas (M = 20 gm/mol). If it is subjected to a process such that pressure exerted is directly proportional to square of volume under normal conditions.

• A. $\frac{10}{3}R$
• B. $\frac{20}{3}R$
• C. $\frac{17}{6}R$
• D. $\frac{17}{3}R$

Answer 1

The correct option is B $\frac{20}{3}R$

$P\propto V^2$
Triatomic non linear gas
$P=K{V}^2$
$C_v=(3+3)\frac{R}{2}=3R$(at moderate temperature)
$P{V}^{-2}=K$
Compare $P{V}^x=K\Rightarrow x=-2$
$C_m=C_v+\frac{R}{1-x}$
$=3R+\frac{R}{1+2}=3R+\frac{R}{3}=\frac{10R}{3}$
$n=\frac{\text{given mass}}{\text{molar mass}}$
$C=n{C}_m=2\times C_m$
$C=\frac{20}{3}R$