Question

Calculate the heat absorbed by the system undergoing a cyclic process as shown in the figure below.

• A. $40\pi \text{J}$
• B. $-7\pi \text{J}$
• C. $7\pi \text{J}$
• D. $-40\pi \text{J}$

Answer 1

The correct option is A $40\pi \text{J}$

From the figure, we can deduce that, the given cyclic process is in clockwise direction, so the work done during the cyclic process is positive.
Workdone during the cyclic process = Area under the curve.
$\therefore$ Workdone$W=\pi \times \left(\frac{600-200}{2}\right)\times \left(\frac{600-200}{2}\right)\times [{10}^{-6}\times {10}^3]=+40\pi \text{J}$
In a cyclic process, as the initial and final states of the system are same, we can say that,
$\Delta U=0$
Thus, from first law of thermodynamics,
$\Delta Q=W$
So, heat absorbed by the cycle is $+40\pi \text{J}$
Hence, option (a) is the correct answer.