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 $50 \, J$ in magnitude), an isothermal compression (work is $30 \, J$ in magnitude), an adiabatic expansion (work is $40\, J$ in magnitude) and then an adiabatic compression (work is $25\, J$ in magnitude). Find the magnitude of change in internal energy (in $ J$) in path $2$, i.e., in path $AFGE$.

Answer 1

$\Delta U_{A B}+\Delta U_{B C}+\Delta U_{C D}+\Delta U_{D E}=\Delta U_{i f} $
$0+\left(-W_{B C}\right)+0+\left(-W_{D E}\right)=\Delta U_{i f}$
$-40\, J +(-(-25))=\Delta U_{-i f} $
$-40+25=\Delta U_{-i f} $
$\Delta U_{i f}=-15\, J$
(For path $A B$ : Isothermal process
$\left.Q_{A B}=W_{A B}=50 \,J \right)$