Question

Calculate specific heat capacity of a diatomic ideal gas (Molar mass = 11 gm / mol ) at constant pressure, if it is subjected to a process such that pressure exerted is directly proportional to cube of the volume.
[R = 2 Cal / mol K]

• A. 5 Cal / mol K
• B. 11 Cal / g K
• C. 0.5 Cal / g K
• D. 0.5 Cal / mol K

Answer 1

The correct option is C 0.5 Cal / g K

We know that
$P{V}^x=K$...........(1)
According to question $p\propto v^3\Rightarrow p=k{v}^3$
or $p{v}^{-3}=K$
From equation (1) and (2) we get x = -3
$\because C_{p,m}=C_{v,m}+\frac{R}{1-x}{C}_{p,m}=\frac{5R}{2}+\frac{R}{4}=\frac{22R}{8}=\frac{22\times 2}{8}\text{Cal}{\text{K}}^{-1}{\text{mole}}^{-1}$
Heat capacity $=\frac{C_{p,m}}{\text{molar mass}}=\frac{5.5}{11}=\frac{1}{2}$
= 0.5 cal / g K