Question

In changing the state of a gas adiabatically from an equilibrium state A to another equilibrium state B an amount of work equal to $22.3J$ is done on the system. If the gas is taken from state A to B via a process in which the net heat absorbed by the system is $9.35cal$ then net work done by the system in the later case is:
(Take $1cal=4.2J)$

• A. $15J$
• B. $16J$
• C. $17J$
• D. $18J$

Answer 1

The correct option is C $17J$

In the first case, the process is adiabatic. i.e $\Delta Q=0$

$22.3J$ work is done on the system i.e. $\Delta W=-22.3J$

$\Delta Q=\Delta U+\Delta W$

$0=\Delta u-22.3$

$\Delta u=22.3J$

In the later process, the initial and final states are same as those in the former process, $\Delta u$ will remain same for the later case.

In the later case, net heat absorbed by the heat is $9.35cal$

$\Delta Q=9.35\times 4.2$

$\Delta Q=39.3J$

$\Delta W=\Delta Q-\Delta u$

$\Delta W=39.3-22.3$

$\Delta W=17J$

The net work done in the system in this case is $17J$.