Question

A gas is taken through the cycle \(A \rightarrow B \rightarrow C \rightarrow A,\) as shown. What is the net work done by the gas?

• A. Zero
• B. -2000 J
• C. 2000 J
• D. 1000 J

Answer 1

The Correct Option is D

 To calculate the net work done by the gas in the cycle \(A \rightarrow B \rightarrow C \rightarrow A\), we need to understand the nature of each process involved in the cycle as displayed in the pressure-volume (P-V) diagram.

The net work done by the gas in a cycle is equal to the area enclosed by the cycle on the P-V diagram. Let's break down each step:

1. Process \(A \rightarrow B\): This is an isochoric (constant volume) process. Since the volume doesn't change, no work is done in this process.
2. Process \(B \rightarrow C\): This is an isobaric (constant pressure) process with pressure \(P_B = P_C = 7 \times 10^5 \, \text{Pa}\).
   • \(V_C = 8 \times 10^{-3}\, \text{m}^3\)
   • \(V_B = 4 \times 10^{-3}\, \text{m}^3\)
3. Process \(C \rightarrow A\): This is another isobaric process, with pressure \(P_C = P_A = 3 \times 10^5 \, \text{Pa}\).
   • \(V_A = 2 \times 10^{-3}\, \text{m}^3\)
   • \(V_C = 8 \times 10^{-3}\, \text{m}^3\)

The net work done by the gas in the cycle is the algebraic sum of the work done in each process:

\(W_{\text{net}} = W_{BC} + W_{CA} = 2800 + (-1800) = 1000 \, \text{J}\)

Thus, the correct answer is 1000 J.