Question

For a gas if ratio of specific heats at constant pressure and volume is \( \gamma \), then value of degrees of freedom is:

• A. \( 3\gamma - 1 \)
• B. \( 2\gamma - 1 \)
• C. \( \frac{9}{2} (\gamma - 1) \)
• D. \( \frac{5}{2} (\gamma - 1) \)

Hint:

The degrees of freedom of a gas are related to the ratio of specific heats \( \gamma \).

Answer 1

The Correct Option is B

Step 1: Relation between \( \gamma \) and degrees of freedom.
The ratio \( \gamma \) is given by: \[ \gamma = \frac{C_P}{C_V} \] where \( C_P \) and \( C_V \) are the specific heats at constant pressure and volume, respectively. The degrees of freedom \( f \) can be related to \( \gamma \) by: \[ \gamma = \frac{f + 2}{f} \] Thus, \( f = 2\gamma - 1 \).
Thus, the correct answer is (2).