Question

A polyatomic gas with six degrees of freedom does $25\text{J}$ of work when it is expanded at constant pressure. The heat given to the gas is

• A. $100\text{J}$
• B. $150\text{J}$
• C. $200\text{J}$
• D. $250\text{J}$

Answer 1

The correct option is A $100\text{J}$

Degree of freedom, $f=6$
$C_V=\frac{fR}{2}=3R$
$C_V=$ constant volume
$C_P=C_V+R=4R$
$C_P=$ constant pressure
Also, work done $=\Delta W=25\text{J}$
Thus, for isobaric process,
Applying first law,
$\Delta Q=\Delta U+\Delta W$
$n{C}_P\Delta T=n{C}_V\Delta T+\Delta W$
$4nR\Delta T=3nR\Delta T+25\text{J}$
$nR\Delta T=25\text{J}$
So, $\Delta Q=4\times 25=100\text{J}$