Question

Figure below shows two paths that may be taken by a gas to go from a state A to a state C. In process AB, 400J of heat is added to the system and in process BC, 100J of heat is added to the system. The heat absorbed by the system in the process AC will be: 

• A. \(500\,\text{J}\)
• B. \(460\,\text{J}\)
• C. \(300\,\text{J}\)
• D. 380J

Hint:

Internal energy change depends only on initial and final states, not on the path.

Answer 1

The Correct Option is D

Step 1: From the P-V diagram, internal energy change Δ U between states A and C is path independent.
Step 2: Along path A → B → C: QAB+QBC=400+100=500J
Step 3: Work done: WAB=0 (constant volume) WBC=PΔ V = 6×10⁴ × (4-2)×10⁻3 = 120J
Step 4: Change in internal energy: Δ U = Q - W = 500 - 120 = 380J
Step 5: Along path A → C: QAC=Δ U + WAC From the diagram, WAC=0, hence QAC=380J