When the state of a gas adiabatically changed from an equilibrium state A to another equilibrium state B an…
When the state of a gas adiabatically changed from an equilibrium state A to another equilibrium state B an amount of work done on the stystem is $35 \mathrm{~J}$. If the gas is taken from state $\mathrm{A}$ to $\mathrm{B}$ via process in which the net heat absorbed by the system is $12 \mathrm{cal}$, then the net work done by the system is $(1 \mathrm{cal}=4.19 \mathrm{~J})$
$13.2 \mathrm{~J}$
$15.4 \mathrm{~J}$
$12.6 \mathrm{~J}$
$16.8 \mathrm{~J}$
Solution
In the first-case adiabatic change, $\Delta \mathrm{Q}=0, \Delta \mathrm{W}=-35 \mathrm{~J}$
From $1^{\text {st }}$ law of thermodynamics, $\Delta \mathrm{Q}=\Delta \mathrm{U}+\Delta \mathrm{W}$
or $\quad 0=\Delta \mathrm{U}-35$
$\therefore \Delta \mathrm{U}=35 \mathrm{~J}$
In the second case $\Delta \mathrm{Q}=12 \mathrm{cal}=12 \times 4.2 \mathrm{~J}=50.4 \mathrm{~J}$
$\Delta \mathrm{W}=\Delta \mathrm{Q}-\Delta \mathrm{U}=50.4-35=15.4 \mathrm{~J}$
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