Question

How much heat energy should be added to the gaseous mixture consisting of $1g$ of hydrogen and $1g$ of helium to raise its temperature from $0^{o}C$ to ${100}^{o}C$ at constant volume? ( in cal )

• A. $325$
• B. $300$
• C. $225$
• D. $250$

Answer 1

The correct option is A $325$

Hydrogen is diatomic. Hence its $C_v=C_{v_1}=2.5R$
Helium is monoatomic.Hence its $C_v$=$C_{v_2}=1.5R$
Thus heat required, $\Delta Q$=$(n_1{C}_{v_1}+n_2{C}_{v_2})\times$ $\Delta T$
Here, $n_1$=number of moles of hydrogen=0.5, $n_2$=number of moles of helium=0.25, $\Delta T$ =change in temperature=$100K$
Hence, $\Delta Q=325cal$