Physics Q31 – JEE-MAIN 2025

Home Physics ThermodynamicsQuestion #523

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

Clue 1 of 3: Definition of Adiabatic Process

An adiabatic process is one where no heat is exchanged between the system and its surroundings.

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Ninja Strategy•Definition-Based Elimination

By recalling the fundamental definition of an adiabatic process ( $Q = 0$ ) and its implications for the First Law of Thermodynamics and molar heat capacity, most options can be quickly eliminated.

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● Video Walkthrough

Step 1: Define Adiabatic Process✦ Active

An adiabatic process is a thermodynamic process that occurs without transfer of heat or mass between the thermodynamic system and its surroundings. Therefore, for an adiabatic process, the heat exchange $Q = 0$ .

Step 2: Apply First Law of Thermodynamics○ Expand

According to the First Law of Thermodynamics, $Δ U = Q - W$ , where $Δ U$ is the change in internal energy, $Q$ is the heat added to the system, and $W$ is the work done by the system. Since $Q = 0$ for an adiabatic process, the equation becomes:

Δ U = - W

This means the increase in internal energy is equal to the negative of the work done by the gas. Option 1 states "Work done by the gas equals the increase in internal energy" ( $W = Δ U$ ), which is generally false unless $W = 0$ and $Δ U = 0$ . Option 2 states "The internal energy of the gas decreases as the temperature increases". For an ideal gas, internal energy $U$ is directly proportional to temperature $T$ ( $U = n C_{v} T$ ), so an increase in temperature leads to an increase in internal energy. Thus, Option 2 is false.

💡 Teacher's Secret Hint

Remember the sign convention for work done: $W$ is work done *by* the system.

Step 3: Evaluate Molar Heat Capacity○ Expand

The molar heat capacity $C$ is defined as the heat required to raise the temperature of one mole of a substance by one degree Celsius (or Kelvin). Mathematically, $C = \frac{1}{n} \frac{d Q}{d T}$ . Since $d Q = 0$ for an adiabatic process, the molar heat capacity for an adiabatic process is:

C = \frac{1}{n} \frac{0}{d T} = 0

Therefore, Option 3, "The molar heat capacity is zero", is true. Option 4, "The molar heat capacity is infinite", would imply $d T = 0$ for a non-zero $d Q$ , which corresponds to an isothermal process, not an adiabatic one.

💡 Teacher's Secret Hint

Distinguish between specific heat capacities for different processes (e.g., $C_{p}$ , $C_{v}$ ) and the general definition of heat capacity for a specific process.

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Physics Question 31 – JEE-MAIN 2025

Clue 1 of 3: Definition of Adiabatic Process

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