Question

The difference of \( C_P \) and \( C_V \) of a substance is:

• A. Positive, finite and variable quantity
• B. Negative, finite and constant quantity
• C. Positive, finite and constant quantity
• D. Negative, finite and variable quantity

Hint:

For ideal gases, always remember: \( C_P - C_V = R \). The difference is constant and positive.

Answer 1

The Correct Option is C

Step 1: Definitions of Heat Capacities
- \( C_P \): Heat capacity at constant pressure.
- \( C_V \): Heat capacity at constant volume.
For any substance, especially gases, \( C_P \) is always greater than \( C_V \), because at constant pressure, the system also performs expansion work, requiring more heat input. Step 2: Theoretical Relationship
For an ideal gas, the relationship between \( C_P \) and \( C_V \) is given by: \begin{equation} C_P - C_V = nR \end{equation} where:
\( n \) is the number of moles of the gas, and
\( R \) is the universal gas constant. Thus, the difference is positive, finite, and for an ideal gas, constant (as \( R \) is constant and \( n \) is fixed). Step 3: Evaluating the Options
- (A) Incorrect — it's not variable for ideal gases.
- (B) Incorrect — the difference is not negative.
- (C) Correct — matches theoretical result.
- (D) Incorrect — wrong in sign and variability. Conclusion: The difference \( C_P - C_V \) is a positive, finite, and constant quantity for an ideal gas.