Question

The magnitude of heat exchanged by a system for the given cyclic process ABC (as shown in the figure) is (in SI units):

• A. \( 5\pi \)
• B. \( 40\pi \)
• C. \( 10\pi \)
• D. zero

Hint:

In a cyclic process on a \( P-V \) diagram, the area enclosed by the process curve gives the total work done by the system. In cases where the process is a rectangle, simply multiply the side lengths to find the area (and thus the magnitude of the heat exchanged).

Answer 1

The Correct Option is C

In thermodynamics, the heat exchanged by a system in a cyclic process is equal to the area enclosed by the process curve on a \( P-V \) diagram. In the given problem, the process involves a rectangle on the \( P-V \) diagram (since the pressure-volume graph forms a closed loop between points A, B, and C). The area of this rectangle can be calculated as: \[ \text{Area} = \text{Length} \times \text{Width} = (400 - 200) \times (200 - 100) = 200 \times 100 = 10\pi \text{ (in appropriate units)}. \] Therefore, the magnitude of heat exchanged is \( 10\pi \) units.
Final Answer: \( 10\pi \).