Question

A monoatomic gas expands isobarically. The percentage of heat supplied that increases the thermal energy and that involved in doing work for expansion is

• A. $40:60$
• B. $60:40$
• C. $50:50$
• D. none of these

Answer 1

The correct option is B $60:40$

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 (thermal) 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 (thermal) 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 $=\frac{3}{2}$ which is 60:40, hence option B is correct