JEE Main 2025 Apr 2 Shift 1, Physics Q12: Thermodynamic Processes

JEE Main2025Apr 2, Shift 1Physics

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

A
The molar heat capacity is infinite
B
Work done by the gas equals the increase in internal energy
C
The molar heat capacity is zero
D
The internal energy of the gas decreases as the temperature increases

Solution

For an adiabatic process $d Q = 0$ . The molar heat capacity is defined as $C = \frac{d Q}{n d T}$ , so:

$C_{adiabatic} = \frac{0}{n d T} = 0$

Checking the other options:

(2) The first law gives $d Q = d U + d W$ . With $d Q = 0$ , $d W = - d U$ , so the work done by the gas equals the decrease (not increase) in internal energy. Wrong.

(4) From $d U = \frac{f}{2} n R d T$ , $U$ increases as $T$ increases. Wrong.

(1) An infinite molar heat capacity corresponds to an isothermal process. Wrong.

$∴$ Option (3) is correct.

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JEE Main 2025 Apr 2 Shift 1, Physics Q12: Thermodynamic Processes

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