Question

When a monoatomic gas expands at constant pressure, the percentage of heat supplied that increases the internal energy of the gas and that which is involved in expansion is :

• A. 75%, 25%
• B. 25%, 75%
• C. 60%, 40%
• D. 40%, 60%

Answer 1

The correct option is C 60%, 40%

For an isobaric process $Pressure=Constant$
Total heat supplied to system $Q=n{C}_p\Delta T$
Degrees of Freedom $f$ for mono-atomic gas $=3$
$C_v=\frac{fR}{2}=\frac{3R}{2}$
$C_p=C_v+R=\frac{fR}{2}+R=\frac{5R}{2}$
$Q=\frac{5R\Delta T}{2}$
Heat needed to increase the Temperature $=\Delta U=n{C}_v\Delta T=\frac{3R\Delta T}{2}$
% heat to increase the temp $=\frac{\Delta U}{Q}\ast 100=60$
Heat required for expansion $=W=P\Delta V=nR\Delta T$
% heat used for expansion $=\frac{W}{Q}\ast 100=40$