Question

An ideal gas is heated at constant pressure and absorbs amount of heat $Q$. If the adiabatic exponent is $ \gamma $ , then the fraction of heat absorbed in raising the internal energy and performing the work is

• A. $ 1-\frac{1}{\gamma } $
• B. $ 1+\frac{1}{\gamma } $
• C. $ 1-\frac{2}{\gamma } $
• D. $ 1+\frac{2}{\gamma } $

Answer 1

Answer: (A)

Heat absorbed by the system at constant pressure $Q=n C_{p} \Delta T$ and change in internal energy
$\Delta U = nC_V \Delta T $
$W = Q -\Delta U$
fraction $=\frac{W}{Q}=\frac{Q-\Delta U}{Q}=1-\frac{\Delta U}{Q} $
$=1-\frac{\Delta U}{Q}=\left(1-\frac{1}{\gamma}\right)$