Question

When $1mole$ of a monoatomic gas expands at constant pressure the ratio of the heat supplied that increases the internal energy of the gas and that used in expansion is

• A. $\frac{2}{3}$
• B. $\frac{3}{2}$
• C. $0$
• D. $\infty$

Answer 1

The correct option is B $\frac{3}{2}$

Heat supplied to one mole of gas in a constant pressure process is given by: $Q=C_p\Delta T$
Change in the internal energy of gas is given by:$\Delta U=C_v\Delta T$

The ratio of heat that goes into increasing the internal energy is:
$\frac{\Delta U}{Q}=\frac{C_v}{C_p}=\frac{1}{\gamma }$

For a mono atomic gas $\gamma =\frac{5}{3}$
So, $\frac{3}{5}$ ratio of heat goes into increasing the internal energy, and the rest goes into expansion work = $\frac{2}{5}$ of heat supplied

Hence, the ratio of heat supplied to increase internal energy by heat supplied to do expansion is $=\frac{3}{2}$