An ideal gas expands against constant external pressure of 2 bar from 5 lit to 8 lit and absorbs 10 kJ of…
An ideal gas expands against constant external pressure of 2 bar from 5 lit to 8 lit and absorbs 10 kJ of heat. What is $\Delta \mathrm{U}$ of the system?
10600 J
9400 J
-10600 J
-9400 J
Solution
$\begin{array}{ll}
& W=-P_{\text {ext }} \times \Delta V=-2 \times(8-5)=-6 \mathrm{~L} \text { bar } \\
& 1 \mathrm{~L} \mathrm{bar}=100 \mathrm{~J} \\
\therefore \quad & W=-600 \mathrm{~J}=-0.6 \mathrm{~kJ} \quad(\because 1 \mathrm{~kJ}=1000 \mathrm{~J}) \\
& Q=+10 \mathrm{~kJ}
\end{array}$ According to the first law of thermodynamics,
$\begin{aligned}
& \Delta \mathrm{U}=\mathrm{Q}+\mathrm{W} \\
& \therefore \quad \Delta \mathrm{U}=+10 \mathrm{~kJ}+(-0.6 \mathrm{~kJ})=9.4 \mathrm{~kJ}=9400 \mathrm{~J}
\end{aligned}$