A system is taken from state $a$ to state $c$ by two paths $a d c$ and $a b c$ as shown in the figur

Question

A system is taken from state $a$ to state $c$ by two paths $a d c$ and $a b c$ as shown in the figure. The internal energy at $a$ is $U_{a}=10 \mathrm{~J}$. Along the path $a d c$ the amount of heat absorbed $d Q_{1}=50 \mathrm{~J}$ and the work obtained $d W_{1}=20 \mathrm{~J}$ whereas along the path $a b c$ the heat absorbed $d Q_{2}=36 \mathrm{~J}$. The amount of work along the path $a b c$ is\

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(d) : According to first law of thermodynamics, $\delta Q=\delta U+\delta W$\ Along the path $a d c$, change in internal energy, $$ \begin{aligned} & \delta U_{1}=\delta Q_{1}-\delta W_{1} \ & =50 \mathrm{~J}-20 \mathrm{~J}=30 \mathrm{~J} \end{aligned} $$ Along the path $a b c$,\ Change in internal energy,\ $\delta U_{2}=\delta Q_{2}-\delta W_{2}$\ $\delta U_{2}=36 \mathrm{~J}-\delta W_{2}$\ As change in internal energy is path independent.\ $	herefore \delta U_{1}=\delta U_{2} \Rightarrow 30 \mathrm{~J}=36 \mathrm{~J}-\delta W_{2}$\ $\delta W_{2}=36 \mathrm{~J}-30 \mathrm{~J}=6 \mathrm{~J}$\