MCQMediumJEE 2026Internal Energy & Enthalpy

JEE Chemistry 2026 Question with Solution

Match the LIST-I with LIST-II.

Table with List-I thermodynamic processes A to D and List-II magnitudes in kJ labeled I equals 4, II equals 11.5, III equals 6, and IV equals 7.

Choose the correct answer from the options given below:

  • A

    A-III, B-II, C-IV, D-I

  • B

    A-II, B-I, C-III, D-IV

  • C

    A-I, B-II, C-III, D-IV

  • D

    A-II, B-III, C-I, D-IV

Answer

Correct answer:B

Step-by-step solution

Standard Method

Given: A matching question on thermodynamic processes and their magnitudes in kJ\text{kJ}.

Find: The correct correspondence between A, B, C, D and I, II, III, IV.

For A: reversible isothermal expansion of 22 mol ideal gas from 2dm32 \, \text{dm}^3 to 20dm320 \, \text{dm}^3 at 300K300 \, \text{K}.

W=nRTln(V2V1)W = nRT \ln\left(\frac{V_2}{V_1}\right) W=2×8.314×300×ln(10)11.5kJW = 2 \times 8.314 \times 300 \times \ln(10) \approx 11.5 \, \text{kJ}

Thus, A \rightarrow II.

For B: irreversible isothermal expansion against constant external pressure.

W=Pext(V2V1)=3×(31)=6kJW = P_{\text{ext}}(V_2 - V_1) = 3 \times (3 - 1) = 6 \, \text{kJ}

Thus, B \rightarrow I.

For C: change in internal energy.

ΔU=nCVΔT=1×32R×3206kJ\Delta U = n C_V \Delta T = 1 \times \frac{3}{2}R \times 320 \approx 6 \, \text{kJ}

Thus, C \rightarrow III.

For D: change in enthalpy at constant pressure.

ΔH=nCPΔT=1×52R×3377kJ\Delta H = n C_P \Delta T = 1 \times \frac{5}{2}R \times 337 \approx 7 \, \text{kJ}

Thus, D \rightarrow IV.

So the final matching is

A-II, B-I, C-III, D-IV\boxed{\text{A-II, B-I, C-III, D-IV}}

Therefore, the correct option is B.

Process-wise Identification

Given: Each item in List-I asks for either work, internal energy change, or enthalpy change.

Find: Which magnitude in List-II matches each process.

  1. For a reversible isothermal process of an ideal gas, use the logarithmic work expression.
  2. For an irreversible expansion against constant external pressure, use PextΔVP_{\text{ext}}\Delta V.
  3. For change in internal energy, use ΔU=nCVΔT\Delta U = nC_V\Delta T.
  4. For change in enthalpy, use ΔH=nCPΔT\Delta H = nC_P\Delta T.

Applying these:

  • A gives 11.5kJ11.5 \, \text{kJ}, so A \rightarrow II.
  • B gives the value marked in the solution as I.
  • C gives about 6kJ6 \, \text{kJ}, so C \rightarrow III.
  • D gives about 7kJ7 \, \text{kJ}, so D \rightarrow IV.

Hence the correct sequence is A-II, B-I, C-III, D-IV, which corresponds to Option B.

Common mistakes

  • Using the irreversible work formula for the reversible isothermal process in A is incorrect because reversible isothermal work depends on the logarithmic volume ratio. Use W=nRTln(V2V1)W = nRT \ln\left(\frac{V_2}{V_1}\right) for A instead.

  • Assuming ΔU=0\Delta U = 0 for process C is wrong because that result applies to an isothermal ideal-gas process, not to the adiabatic case with a stated temperature change. Here you must use ΔU=nCVΔT\Delta U = nC_V\Delta T.

  • Confusing CVC_V and CPC_P leads to interchanging C and D. Internal energy change uses CVC_V, while enthalpy change at constant pressure uses CPC_P.

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