Question

Figure below shows two paths that may be taken by a gas to go from state A to 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 is path independent • Heat depends on the path via work done Always compute Δ U first.

Answer 1

The Correct Option is B

Step 1: From the PV-diagram: Work done in process AB = 0 (constant volume).
Step 2: Work done in process BC: WBC=PΔ V =6×10⁴ × (4-2)×10⁻3 =120J
Step 3: Total heat added in AB+BC: QABC=400+100=500J
Step 4: Change in internal energy: Δ U = Q - W = 500 - 120 = 380J
Step 5: Work done in direct process AC (average pressure method): WAC=((2+6)×10⁴)/(2)×(4-2)×10⁻3 =80J
Step 6: Heat absorbed in process AC: QAC=Δ U + WAC =380+80=460J