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In an adiabatic process, which of the following statements is true?

Asked in JEE Main 2nd April 1st Shift 2025 · Molar Specific Heats and Degrees of Freedom

(1) The molar heat capacity is infinite
(2) The internal energy of the gas decreases as the temperature increases
(3) Work done by the gas equals the increase in internal energy
(4) The molar heat capacity is zero

Answer: (4) The molar heat capacity is zero

Step-by-step solution

Molar heat capacity is C=Q/(nΔ T).

An adiabatic change has Q=0 while Δ T e0, so C=0.

Why the other options are wrong

(1) comes from infinite C belongs to the isothermal process, where Δ T=0 with Q e0
(2) comes from internal energy of an ideal gas rises with temperature, never falls
(3) comes from the first law gives W=-Δ U here, not +Δ U

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