Question

Heat energy absorbed by a system going through the cyclic process shown in the figure is: 

• A. \( 10^7 \pi \) J
• B. \( 10^4 \pi \) J
• C. \( 10^2 \pi \) J
• D. \( 10^{-3} \pi \) J

Hint:

The work done in a cyclic process equals the area enclosed in the P-V diagram. For an elliptical process, use \( W = \pi \times a \times b \).

Answer 1

The Correct Option is C

Step 1: Understanding the Cyclic Process 
The work done in a cyclic process is given by the area enclosed by the cycle in a Pressure-Volume (P-V) diagram. The shape shown in the given diagram is approximately an ellipse. 
Step 2: Area of an Ellipse in P-V Diagram 
The formula for the area of an ellipse is: \[ A = \pi \times a \times b \] where: - \( a \) is the semi-major axis,
- \( b \) is the semi-minor axis.
Step 3: Extracting Values from the Diagram 
From the diagram:
- The pressure range extends from 10 kPa to 30 kPa, so the semi-major axis is: \[ a = \frac{30 - 10}{2} = 10 { kPa}. \] - The volume range extends from 10 L to 30 L, so the semi-minor axis is: \[ b = \frac{30 - 10}{2} = 10 { L}. \] Step 4: Calculating the Work Done 
\[ W = \pi \times 10 \times 10. \] \[ W = 100\pi { J}. \] Step 5: Conclusion 
Thus, the heat energy absorbed by the system in the cyclic process is: \[ \mathbf{10^2 \pi} { J}. \]