For a gas if ratio of specific heats at constant pressure and volume is γ then value of degrees of freedom is

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;- 1/2&gamma;-1) (B) (2/&gamma;-1) (C) (9/2)(&gamma;-1) (D) (25/2)(&gamma;-1)

Tardigrade Admin · Accepted Answer

&gamma; =1 +(2/f), ⇒ &gamma; -1 =(2/f) ⇒ f =(2/&gamma; -1)

Q. For a gas if ratio of specific heats at constant pressure and volume is $γ$ then value of degrees of freedom is

$\frac{3 γ - 1}{2 γ - 1}$

$\frac{2}{γ - 1}$

$\frac{9}{2} (γ - 1)$

$\frac{25}{2} (γ - 1)$

$γ = 1 + \frac{2}{f}$ ,
$\Rightarrow γ - 1 = \frac{2}{f}$
$\Rightarrow f = \frac{2}{γ - 1}$

Q. For a gas if ratio of specific heats at constant pressure and volume is γ then value of degrees of freedom is

2γ−13γ−1​

γ−12​

29​(γ−1)

225​(γ−1)