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)

$1-\frac{1}{\gamma }$

Heat absorbed by the system at constant pressure $Q=n{C}_p\Delta T$ and
change in internal energy
$\Delta U=n{C}_V\Delta T$
$W=Q-\Delta U$
fraction $=\frac{W}{Q}=\frac{Q-\Delta U}{Q}=1-\frac{\Delta U}{Q}$
$=1-\frac{\Delta U}{Q}=(1-\frac{1}{\gamma })$