A gas undergoes change from state $\mathrm{A}$ to state $\mathrm{B}$. In this process, the heat absorbed and work done by the gas is $5 \mathrm{J} \text{and} 8 \mathrm{J}$, respectively. Now gas is brought back to $\mathrm{A}$ by another process during which $3 \mathrm{J}$ of heat is evolved. In this reverse process of $\mathrm{B} \mathrm{to} \mathrm{A}$.

• A

  $6 \mathrm{J}$of the work will be done by the gas
• Correct answer
  B

  $6 \mathrm{J}$ of the work will be done by the surroundings on gas
• C

  $10 \mathrm{J}$ of the work will be done by the surroundings on gas
• D

  $10 \mathrm{J}$ of the work will be done by the gas

Solution

$\begin{array}{l}\mathrm{for} \mathrm{A} \mathrm{to} \mathrm{B}\\ \mathrm{q}=5\\ \mathrm{W}=\mathrm{ }-8 \mathrm{J},\\ {\mathrm{\Delta U}}_{\mathrm{AB}}=\mathrm{dq}+\mathrm{dw}=5-8\\ {\mathrm{\Delta U}}_{\mathrm{AB}}=-3\end{array}$



$\begin{array}{l}\mathrm{for} \mathrm{B} \mathrm{to} \mathrm{A}\\ {\mathrm{\Delta U}}_{\mathrm{BA}}=\mathrm{dq}+\mathrm{dw}\\ {\mathrm{\Delta U}}_{\mathrm{BA}}=\mathrm{ }+3\\ 3=-3 +{\mathrm{W}}_{\mathrm{BA}} \\ {\mathrm{W}}_{\mathrm{BA}}=6 \mathrm{J}\end{array}$
 

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