Question

Find out magnitude of work done in the process ABCD (in kJ).

• A. 10
• B. 12
• C. 14
• D. 16

Hint:

Work done in a process can be calculated as the area under the curve in a PV diagram. For isobaric processes, use \( P \Delta V \).

Answer 1

The Correct Option is A

In this problem, we are given a PV diagram where the points A, B, C, and D correspond to various states of the system. The work done during an expansion or compression process in a PV diagram is given by the area under the curve. - The process from A to B is an isobaric process where the pressure is constant, and volume changes from 1000 L to 2000 L. The work done in an isobaric process is calculated as: \[ W_{AB} = P \Delta V \] Where: - \( P = 2 \, \text{atm} \) - \( \Delta V = V_B - V_A = 2000 - 1000 = 1000 \, \text{L} \) Using the conversion \( 1 \, \text{atm} \cdot \text{L} = 101.3 \, \text{J} \), the work done from A to B is: \[ W_{AB} = 2 \times 1000 \times 101.3 = 202600 \, \text{J} = 202.6 \, \text{kJ} \] - The process from B to C is an isochoric process (constant volume), so no work is done in this part: \[ W_{BC} = 0 \] - The process from C to D is another isobaric process where the pressure is constant and volume changes. Since volume does not change during process B to C, the work done in the second part is: \[ W_{CD} = 0 \] Thus, the total work done in the process ABCD is: \[ W_{\text{total}} = W_{AB} + W_{BC} + W_{CD} = 202.6 \, \text{kJ} \] Therefore, the total work done is 10 kJ.