Question

Assertion (A) Specific heat of a gas at constant pressure is greater than its specific heat at constant volume.

Reason (R) At constant pressure, some amount of heat is spent in expansion of the gas.

(NCERT Pg. 254)

• A. Both Assertion (A) and Reason (R) are true, and Reason (R) is the correct explanation for Assertion (A).
• B. Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation for Assertion (A).
• C. Assertion (A) is true, but Reason (R) is false.
• D. Assertion (A) is false, but Reason (R) is true.

Answer 1

Answer: (A)

Both Assertion (A) and Reason (R) are true, and Reason (R) is the correct explanation for Assertion (A).

Answer 2

Explanation:

1. Assertion (A): The statement that the specific heat of a gas at constant pressure ($C_P$) is greater than its specific heat at constant volume ($C_V$) is true. This is a fundamental principle in thermodynamics.

2. Reason (R): The statement that at constant pressure, some heat is spent in the expansion of the gas is also true. According to the First Law of Thermodynamics, $\Delta Q = \Delta U + \Delta W$, where $\Delta Q$ is the heat supplied, $\Delta U$ is the change in internal energy, and $\Delta W$ is the work done by the gas. At constant pressure, the gas expands, doing work ($\Delta W = P\Delta V$).

3. Reason (R) explains Assertion (A): At constant volume, $\Delta Q_V = \Delta U$. At constant pressure, $\Delta Q_P = \Delta U + P\Delta V$. Since $P\Delta V > 0$, it follows that $\Delta Q_P > \Delta Q_V$ for the same $\Delta T$. Therefore, $C_P$ must be greater than $C_V$, and Reason (R) correctly explains Assertion (A).