Question

A diatomic ideal gas initially at $273K$ is given $100cal$ heat due to which system did $209J$ work. Molar heat capacity $\left(C_m\right)$ of gas for the process is:

• A. $\frac{3}{2}R$
• B. $\frac{5}{2}R$
• C. $\frac{5}{4}R$
• D. $5R$

Answer 1

The correct option is D $5R$

From first law of thermodynamics :
$\Delta U$ = $q+W$
and $△U=n{C}_v△T$
so,
$n{C}_v△T=100\times 4.2-209=420-209=211Jn\times \frac{5R}{2}\times △T=211n△T=\frac{211\times 2}{5R}$
molar heat capacity is given as:
$C_m=\frac{q}{n△T}=\frac{420}{211\times 2}\times 5R\approx 5R$