Question

A system is taken fromstate $a$ to state $c$ by two paths $adc$ and $abc$ as shown in the figure. The internal energy at $a$ is $U_a=10J$. Along the path $adc$ the amount of heat heat absorbed $d{Q}_1=50J$ and the work obtained $d{W}_1=20J$ whereas along the path $abc$ the heat absorbed $d{Q}_2=36J$. 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)

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