Question

The average degree of freedom per molecule for a gas are $6$. The gas performs $25J$ of work when it expands at a constant pressure. The heat absorbed by gas is

• A. $75J$
• B. $100J$
• C. $150J$
• D. $125J$

Answer 1

The correct option is B $100J$

For a gas with 'n' degrees of freedom:
$\gamma =1+\frac{2}{n}=1+\frac{2}{6}=\frac{4}{3}$
$C_p=\frac{\gamma R}{\gamma -1}=4R$
$C_v=\frac{R}{\gamma -1}=3R$

Heat supplied for constant pressure process is $n{C}_p\Delta T$

Change in internal energy $n{C}_v\Delta T$
$\frac{\Delta U}{Q}=\frac{C_v}{C_p}=\frac{1}{\gamma }=\frac{3}{4}$

Hence $\frac{W}{Q}=1-\frac{\Delta U}{Q}=\frac{1}{4}$

$\frac{W}{Q}=1-\frac{3}{4}=\frac{1}{4}$

$⟹Q=100J$