Question

A system is taken from state $a$ to state $c$ by two paths $adc$ and $abc$ as shown in the figure. The internal energy at $a$ is $U_a=10 \, J .$ Along the path $adc$ the amount of heat heat absorbed $\delta Q_1=50\, J$ and the work obtained $\delta W_1=20 \, J$ whereas along the path $abc$ the heat absorbed $\delta Q_2=36 \, J .$ The amount of work along the path $abc$ is :

• A. 10 J
• B. 12 J
• C. 36 J
• D. 6 J

Answer 1

Answer: (D)

6 J

Answer 2

According to first law of thermodynamics,
$\delta Q= \delta U+ \delta W$
Along the path adc Change in internal energy,
$\delta U_1= \delta Q_1- \delta W_1$
$= 50\, J -20\, J = 30 \,J$
Along the path abc
Change in internal energy,
$\delta U_2= \delta Q_2- \delta W_2$
$\delta U_2= 36\, J- \delta W_2$
As change in internal energy is path independent.
$\therefore \delta U_1= \delta U_2$
$\therefore 30\, J=36\, J- \delta W_2$
$\delta W_2=36 \, J-30 \, J=6 \, J$