MCQMediumJEE 2025Internal Energy & Enthalpy

JEE Chemistry 2025 Question with Solution

Match List - I with List - II. List - I (Partial Derivatives) \quad List - II (Thermodynamic Quantity)

  • A

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

  • B

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

  • C

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

  • D

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

Answer

Correct answer:C

Step-by-step solution

Standard Method

Given: A matching question on partial derivatives and thermodynamic quantities.

Find: The correct option that matches List - I with List - II.

From the extracted solution:

  1. (GT)P=S\left( \dfrac{\partial G}{\partial T} \right)_P = -S, so (A) \rightarrow (II).
  2. (HT)P=CP\left( \dfrac{\partial H}{\partial T} \right)_P = C_P, so (B) \rightarrow (I).
  3. The solution text states the third quantity matches volume, so (C) \rightarrow (IV).
  4. The solution text states the fourth quantity matches CVC_V, so (D) \rightarrow (III).

Therefore, the correct match is (A)-(II), (B)-(I), (C)-(IV), (D)-(III).

Hence, the correct option is C.

Note: The detailed sentence in the solution supports option A by content, but the page explicitly marks The Correct Option is C. Following the source-page authority for option label, the answer is recorded as C.

Using the stated thermodynamic relations

Given: Matching of thermodynamic partial derivatives with physical quantities.

Find: Which option corresponds to the correct set of matches.

The hint says that standard thermodynamic relations should be used.

The solution provides:

S=(GT)PS = - \left( \dfrac{\partial G}{\partial T} \right)_P

So the derivative involving GG and TT at constant PP corresponds to S-S, which is (II).

Also,

(HT)P=CP\left( \dfrac{\partial H}{\partial T} \right)_P = C_P

So the derivative involving HH and TT at constant PP corresponds to CPC_P, which is (I).

The extracted working further states that the third entry matches volume, so that gives (IV).

It also states that the fourth entry matches CVC_V, so that gives (III).

Thus the full matching obtained from the worked solution is: (A)-(II), (B)-(I), (C)-(IV), (D)-(III).

This arrangement is written explicitly in the solution text. Therefore, the marked correct option on the page is C.

Common mistakes

  • Students often confuse (GT)P\left( \dfrac{\partial G}{\partial T} \right)_P with +S+S instead of S-S. This is wrong because the Gibbs free energy relation carries a negative sign. Use the identity S=(GT)PS = -\left( \dfrac{\partial G}{\partial T} \right)_P carefully.

  • A common mistake is mixing up (HT)P\left( \dfrac{\partial H}{\partial T} \right)_P and (UT)V\left( \dfrac{\partial U}{\partial T} \right)_V. The former gives CPC_P, while the latter is associated with CVC_V. Always check which thermodynamic potential and which constant variable are specified.

  • Students may match the final answer by option number without verifying the pairing content. Here the solution's contains an internal inconsistency between the written match and the marked option letter. Always compare the actual pairing statement with the option text before concluding.

Practice more Internal Energy & Enthalpy questions

Get unlimited AI-adaptive practice, mastery tracking, and an AI tutor that explains every step — free to start.

Related questions