Question

An ideal gas is heated at constant pressure and in this process, it absorbs $Q$ amount of heat. If the adiabatic exponent is $\gamma $ , then the fraction of heat absorbed in 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
$Q=nc_{p}\Delta T$
Change in internal energy $\Delta U=nc_{v}\Delta T$
$W=Q-\Delta U$
$\therefore \, \, \frac{W}{Q}=\frac{Q - \Delta U}{Q}=1-\frac{\Delta U}{Q}$
$=1-\frac{n c_{v} \Delta T}{n c_{p} \Delta T}=1-\frac{c_{v}}{c_{p}}$
$=\left(1 - \frac{1}{\gamma }\right)$