Chemistry Q54 – JEE-MAIN 2026

Home Chemistry ThermodynamicsQuestion #629

Given below are two statements: Statement I: For an ideal gas, heat capacity at constant volume is always greater than the heat capacity at constant pressure. Statement II: In a constant volume process, no work is produced and all the heat withdrawn goes into the chaotic motion and is reflected by a temperature increase of the ideal gas. In the light of the above statements, choose the correct answer from the options given below

Clue 1 of 3: Mayer's Relation

Recall the relationship between molar heat capacities at constant pressure and constant volume for an ideal gas.

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Step 1: Analyze Statement I✦ Active

For an ideal gas, the relationship between molar heat capacity at constant pressure ( $C_{p}$ ) and constant volume ( $C_{v}$ ) is given by Mayer's formula: $C_{p} - C_{v} = R$ , where $R$ is the ideal gas constant. Since $R$ is always positive, it implies that $C_{p} > C_{v}$ . Therefore, heat capacity at constant pressure is always greater than heat capacity at constant volume. Statement I claims that heat capacity at constant volume is greater than heat capacity at constant pressure, which is false.

Step 2: Analyze Statement II○ Expand

In a constant volume (isochoric) process, the change in volume ( $Δ V$ ) is zero. The work done ( $W$ ) is given by $W = - P Δ V$ , so $W = 0$ . This confirms that no work is produced. According to the First Law of Thermodynamics, $Δ U = Q + W$ . Since $W = 0$ , $Δ U = Q$ . For an ideal gas, internal energy ( $U$ ) is directly proportional to temperature ( $T$ ). If heat ( $Q$ ) is withdrawn (meaning added to the system, $Q > 0$ ), then $Δ U > 0$ , which implies an increase in temperature ( $Δ T > 0$ ). The internal energy of an ideal gas is associated with the kinetic energy of its molecules (chaotic motion). Thus, an increase in internal energy due to heat addition leads to an increase in chaotic motion and a temperature increase. Therefore, Statement II is true.

Step 3: Conclusion○ Expand

Based on the analysis, Statement I is false, and Statement II is true. This corresponds to option 4.

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Chemistry Question 54 – JEE-MAIN 2026

Clue 1 of 3: Mayer's Relation

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