JEE Main · 2025 · Shift-IIeasyTHERMO-152

An ideal gas undergoes a cyclic transformation starting from the point A and coming back to the same point by tracing…

Thermodynamics · Class 11 · JEE Main Previous Year Question

Question

An ideal gas undergoes a cyclic transformation starting from the point A and coming back to the same point by tracing the path A→B→C→D→A\text{A} \rightarrow \text{B} \rightarrow \text{C} \rightarrow \text{D} \rightarrow \text{A} as shown in three p-V diagram cases.

Choose the correct option regarding ΔU\Delta U:

(a) ΔU(Case-III)>ΔU(Case-II)>ΔU(Case-I)\Delta U(\text{Case-III}) > \Delta U(\text{Case-II}) > \Delta U(\text{Case-I})

(b) ΔU(Case-I)>ΔU(Case-II)>ΔU(Case-III)\Delta U(\text{Case-I}) > \Delta U(\text{Case-II}) > \Delta U(\text{Case-III})

(c) ΔU(Case-I)>ΔU(Case-III)>ΔU(Case-II)\Delta U(\text{Case-I}) > \Delta U(\text{Case-III}) > \Delta U(\text{Case-II})

(d) ΔU(Case-I)=ΔU(Case-II)=ΔU(Case-III)\Delta U(\text{Case-I}) = \Delta U(\text{Case-II}) = \Delta U(\text{Case-III})

Options
  1. a

    ΔU(Case-III)>ΔU(Case-II)>ΔU(Case-I)\Delta U(\text{Case-III}) > \Delta U(\text{Case-II}) > \Delta U(\text{Case-I})

  2. b

    ΔU(Case-I)>ΔU(Case-II)>ΔU(Case-III)\Delta U(\text{Case-I}) > \Delta U(\text{Case-II}) > \Delta U(\text{Case-III})

  3. c

    ΔU(Case-I)>ΔU(Case-III)>ΔU(Case-II)\Delta U(\text{Case-I}) > \Delta U(\text{Case-III}) > \Delta U(\text{Case-II})

  4. d

    ΔU(Case-I)=ΔU(Case-II)=ΔU(Case-III)\Delta U(\text{Case-I}) = \Delta U(\text{Case-II}) = \Delta U(\text{Case-III})

    ✓
Correct Answerd

ΔU(Case-I)=ΔU(Case-II)=ΔU(Case-III)\Delta U(\text{Case-I}) = \Delta U(\text{Case-II}) = \Delta U(\text{Case-III})

Detailed Solution

🧠 For any cyclic process, ΔU=0\Delta U = 0 because internal energy is a state function A state function depends only on the current state, not the path taken to reach it. Starting and ending at the same point means zero net change — regardless of the shape or direction of the cycle.

All three cases (I, II, III) return the system to point A. Therefore: ΔUCase I=ΔUCase II=ΔUCase III=0\Delta U_{\text{Case I}} = \Delta U_{\text{Case II}} = \Delta U_{\text{Case III}} = 0

⚠️ Trap: Work and heat are path-dependent and will differ across the three cycles. Only state functions like UU, HH, SS, GG are guaranteed zero for any closed cycle.

Answer: (d)\boxed{\text{Answer: (d)}}

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