Question

The ratio of specific heats \( \frac{C_P}{C_V} \) in terms of degrees of freedom (n) is given by:

• A. \( 1 + \frac{n}{3} \)
• B. \( 1 + \frac{2}{n} \)
• C. \( 1 + \frac{1}{n} \)
• D. \( 1 + \frac{n}{2} \)

Hint:

For gases, the ratio \( \frac{C_P}{C_V} \) can be derived from the number of degrees of freedom. In general, the more degrees of freedom, the higher the ratio.

Answer 1

The Correct Option is B

The ratio of specific heats \( \frac{C_P}{C_V} \) is related to the degrees of freedom \( n \) of the gas molecules by the formula: \[ \frac{C_P}{C_V} = 1 + \frac{2}{n} \] This relationship arises from the kinetic theory of gases, where the specific heats depend on the number of degrees of freedom. For an ideal gas, this ratio is known to be \( 1 + \frac{2}{n} \), where \( n \) is the number of degrees of freedom. Thus, the correct option is (B).