Question

In an adiabatic process, no transfer of heat takes place between system and surroundings. Choose the correct option for free expansion of an ideal gas under adiabatic condition from the following.

• A. $q = 0, \Delta T \ne 0$, $W = 0$
• B. $q \ne 0$, $\Delta T = 0$, $W = 0$
• C. $q = 0$, $\Delta T= 0$, $W = 0$
• D. $q = 0$, $\Delta T < 0$, $W \ne 0$

Answer 1

Answer: (C)

For free expansion (i.e. in vacuum), $P_{ext} = 0$.
Thus, $W = -P_{ex}\Delta V=0$
For adiabatic change, $q = 0$
$\therefore \Delta U = q+ W = 0$ which is true for isothermal process where $T$ is constant i.e., $\Delta T = 0$.