JEE Main · 2019 · Shift-IeasyTHERMO-016

An ideal gas is allowed to expand from 1 L to 10 L against a constant external pressure of 1 bar. The work done in kJ…

Thermodynamics · Class 11 · JEE Main Previous Year Question

Question

An ideal gas is allowed to expand from 1 L to 10 L against a constant external pressure of 1 bar. The work done in kJ is:

Options
  1. a

    +10.0

  2. b

    -2.0

  3. c

    -0.9

  4. d

    -9.0

Correct Answerc

-0.9

Detailed Solution

🧠 Work against constant external pressure: w=PextΔVw = -P_{\text{ext}} \cdot \Delta V The gas expands against a fixed opposing pressure, so use the irreversible work formula — not nRTln(Vf/Vi)nRT\ln(V_f/V_i).

🗺️ Calculation w=Pext×(VfVi)=1 bar×(101) L=9 L.barw = -P_{\text{ext}} \times (V_f - V_i) = -1\text{ bar} \times (10 - 1)\text{ L} = -9\text{ L.bar}

Convert using 1 L.bar=0.1 kJ1\text{ L.bar} = 0.1\text{ kJ}: w=9×0.1=0.9 kJw = -9 \times 0.1 = -0.9\text{ kJ}

Negative sign → work is done by the system (expansion).

⚠️ Trap: Don't use the reversible work formula nRTln(Vf/Vi)nRT\ln(V_f/V_i) — that applies only to reversible isothermal expansion. This is expansion against a constant external pressure.

Answer: (c)\boxed{\text{Answer: (c)}}

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