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 a is $U_2=10$ J. Along the path adc the amount of heat heat absorbed $\delta Q_1=50 \mathrm{~J}$ and the work obtained $\delta W_1=20 \mathrm{~J}$ whereas along the path $a b c$ the heat absorbed $\delta Q_2=36 \mathrm{~J}$. The amount of work along the path $a b c$ is:

• A

  $10 \mathrm{~J}$
• B

  $12 \mathrm{~J}$
• C

  $38 \mathrm{~J}$
• Correct answer
  D

  $6 \mathrm{~J}$

Solution

According to $1^{\text {st }} 1$ aw of thermodynamics $\delta Q=\delta V+\delta W$ Along the path adc $\delta U_1=\delta Q_1-\delta W_1=50-20=30 \mathrm{~J}$ then path abc Since change in Internal energy in path in dependence $\begin{aligned} \text {So, } \delta U_1 & =\delta U_2 \\ 30 \mathrm{~J} & =36 \mathrm{~J}-\delta W_2 \\ \Rightarrow \delta W_2 & =36 \mathrm{~J}-30 \mathrm{~J} \\ & =6 \mathrm{~J} \end{aligned}$

Hence, the correct answer is option: 'D'.