Question

A diatomic ideal gas initially at $273$K is given $100$ cal heat due to which system did $209$ J work Molar heat capacity ($C_m$) 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

Answer: (D)

$5R$

$100cal=418J$

$\Delta U=q+w$

$=418-209$

$=209J$

$\Delta Q=C_m\Delta T$

$C_M=\frac{\Delta Q}{\Delta T}$

$=\frac{418\times 5R}{209\times 2}$

$=5R$

$C_V\Delta T=209$

$\Rightarrow \frac{5R}{2}\Delta T=209$

$\Rightarrow \Delta T=\frac{209\times 2}{5R}⟶\left(1\right)$

Molar heat capacity= $5R$