A diatomic gas has an initial internal energy of $80 \mathrm{cal}$. A work of $18 \mathrm{cal}$ is done on…
A diatomic gas has an initial internal energy of $80 \mathrm{cal}$. A work of $18 \mathrm{cal}$ is done on the gas and the gas releases heat energy of $42 \mathrm{~J}$. The final internal energy of the gas is
$20 \mathrm{~J}$
$369.6 \mathrm{~J}$
$54 \mathrm{~J}$
$20 \mathrm{cal}$
Solution
Initial internal energy, $\mathrm{U}_{\mathrm{i}}=80 \mathrm{cal}=80 \times 4.2 \mathrm{~J}$
Work done, $\mathrm{W}=18 \mathrm{cal}=18 \times 4.2 \mathrm{~J}$
Heat released, $Q=42 \mathrm{~J}$
Final internal energy, $\mathrm{U}_{\mathrm{f}}=$ ?
using 1st law of thermodynamics
$
\begin{aligned}
& \Delta Q=\Delta U+\Delta W \\
& \Delta Q=U_i-U_f+\Delta W \\
& 42=336-U_f+75.6 \\
& U_f=369.6 J
\end{aligned}
$