Question

Statement-1: Heat capacity at constant volume is always greater than heat capacity at constant pressure.
Statement-2: At constant volume as work done is zero, heat given to the chaotic motion is reflected by increase in temperature.

• A. Statement-1 and statement-2 both are correct.
• B. Statement-1 is correct but statement-2 is incorrect.
• C. Statement-1 is incorrect but statement-2 is correct.
• D. Both statement-1 and statement-2 are incorrect.

Answer 1

The Correct Option is C

Step 1: Analyze Statement-1.
The heat capacity at constant volume (\( C_V \)) and constant pressure (\( C_P \)) are related by the equation: \[ C_P = C_V + R \] where \( R \) is the gas constant. As \( R \) is positive, it is clear that: \[ C_P>C_V \] Thus, Statement-1 is incorrect because heat capacity at constant volume is always less than or equal to heat capacity at constant pressure, not greater.
Step 2: Analyze Statement-2.
At constant volume, there is no work done, as \( W = P \Delta V = 0 \). The heat added to the system at constant volume only increases the internal energy of the system, which results in an increase in temperature. Therefore, Statement-2 is correct.
Step 3: Conclusion.
Since Statement-1 is incorrect and Statement-2 is correct, the correct answer is (C).
(C) Statement-1 is incorrect but statement-2 is correct.