Question

The figure shows two paths that may be taken by a gas from an initial point $i$ to final point $f$. Path $1$ consists of an isothermal expansion (work is $50J$ in magnitude), an isothermal compression (work is $30J$ in magnitude), an adiabatic expansion (work is $40J$ in magnitude) and then an adiabatic compression (work is $25J$ in magnitude). Find the magnitude of change in internal energy (in $J$) in path $2$, i.e., in path $AFGE$.

Answer 1

As we know internal energy is state function.
Hence, change in internal energy depends on initial and final position.

$\Delta U_{AE}+\Delta U_{BC}+\Delta U_{CD}+\Delta U_{DE}=\Delta U_{if}$

As given process $AB$ is isothermal expansion and $CD$ is isothermal compression.

Therefore, $\Delta U=0$

And process $BC$ is adiabatic expansion and $DE$ is adiabatic compression.

Therefore, $-\Delta U=W$

$0+(-W_{BC})+0+(-W_{DE})=\Delta U_{if}$

$-40J+(-(-25\left)\right)=\Delta U_{if}$

$-40+25=\Delta U_{if}$

$\Delta U_{if}=-15J$

Final answer: $\left(15\right)$