Question

When an ideal mono atomic gas is heated at constant pressure. Fraction of heat energy supplied, which increases the internal energy of gas is:

• A. $\frac{2}{5}$
• B. $\frac{3}{5}$
• C. $\frac{3}{7}$
• D. $\frac{3}{4}$

Answer 1

Answer: (B)

$\frac{3}{5}$

Heat supplied at constant pressure $Q_p=n{C}_p\Delta T$

Change in internal energy $\Delta U=n{C}_v\Delta T$

$\therefore$ Fraction of heat energy supplied $\frac{\Delta U}{Q_p}=\frac{C_v}{C_p}$

But $C_v=\frac{f}{2}R$ and $C_p=(\frac{f}{2}+1)R$ where, $f$ is the degree of freedom

Degree of freedom of mono atomic gas $f=3$

$⟹$ $C_v=\frac{3}{2}R$ and $C_p=(\frac{3}{2}+1)R=\frac{5}{2}R$

$\therefore$ $\frac{\Delta U}{Q_p}=\frac{\frac{3}{2}R}{\frac{5}{2}R}=\frac{3}{5}$