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MCQEasyJEE 2025First Law & Internal Energy

JEE Physics 2025 Question with Solution

Given are statements for certain thermodynamic variables: [(A)] Internal energy, volume VV, and mass MM are extensive variables. [(B)] Pressure PP, temperature TT, and density ρ\rho are intensive variables. [(C)] Volume VV, temperature TT, and density ρ\rho are intensive variables. [(D)] Mass MM, temperature TT, and internal energy are extensive variables. Choose the correct answer from the options given below:

  • A

    (B) and (C) Only

  • B

    (C) and (D) Only

  • C

    (D) and (A) Only

  • D

    (A) and (B) Only

Answer

Correct answer:B

Step-by-step solution

Standard Method

Given: Statements about extensive and intensive thermodynamic variables.

Find: Which pair of statements is correct.

Extensive variables depend on the amount or size of the system. Examples include mass, volume, and internal energy.

Intensive variables do not depend on the amount of material. Examples include pressure, temperature, and density.

Step 1: Analyze the statements

  • (A) Internal energy, volume, and mass are extensive variables. This is correct.
  • (B) Pressure, temperature, and density are intensive variables. This is correct.
  • (C) Volume, temperature, and density are intensive variables. This is incorrect because volume is extensive, while temperature and density are intensive.
  • (D) Mass, temperature, and internal energy are extensive variables. This is incorrect because temperature is intensive.

Therefore, the correct combination is (A) and (B) only.

The solution says "The Correct Option is B" and later concludes "the answer is 2\boxed{2}," but its own step-by-step classification shows that (A) and (B) are the correct statements. Hence the defensible correct option from the given options is D.

Classification Check

Given: The variables are internal energy, volume, mass, pressure, temperature, and density.

Find: Which listed statements match the definitions of extensive and intensive variables.

Use the definitions directly:

Extensive→depends on system size\text{Extensive} \rightarrow \text{depends on system size}Intensive→independent of system size\text{Intensive} \rightarrow \text{independent of system size}

Now classify each quantity:

  • Mass: extensive
  • Volume: extensive
  • Internal energy: extensive
  • Pressure: intensive
  • Temperature: intensive
  • Density: intensive

So:

  • (A) true
  • (B) true
  • (C) false, because volume is not intensive
  • (D) false, because temperature is not extensive

Therefore, the correct option is D, corresponding to (A) and (B) only.

Common mistakes

  • Treating volume as an intensive variable. This is wrong because volume changes with the size of the system. Instead, classify volume as an extensive variable.

  • Treating temperature as an extensive variable. This is wrong because temperature does not depend on how much substance is present. Instead, classify temperature as an intensive variable.

  • Following the listed answer number without checking the definitions. This is wrong because the solution text is internally inconsistent. Instead, verify each statement using the definitions of extensive and intensive variables.

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