Let γ denote the ratio of specific heat for an ideal gas. Then choose the correct expression for number of degrees of freedom of a molecule of the same gas.

Question

Let &gamma; denote the ratio of specific heat for an ideal gas. Then choose the correct expression for number of degrees of freedom of a molecule of the same gas. (A) (25/2)(. &gamma; - 1 .) (B) (3 &gamma; - 1/2 &gamma; - 1) (C) (2/&gamma; - 1) (D) (9/2)(. &gamma; - 1 .)

Tardigrade Admin · Accepted Answer

For, E = Total Energy, f = Degree of freedom of molecule, We Know, Cv= Molar heat capacity at constant volume = (( partial U/ partial T))v=(f/2)R Cp = Molar heat capacity at constant pressure =Cv+R=((. f + 2 .)/2)R

γ = Ratio of specific heats =(Cp/Cv)=(f + 2/f) ⇒ f=(2/γ - 1)

Q. Let $γ$ denote the ratio of specific heat for an ideal gas. Then choose the correct expression for number of degrees of freedom of a molecule of the same gas.

$\frac{25}{2} (γ - 1)$

$\frac{3 γ - 1}{2 γ - 1}$

$\frac{2}{γ - 1}$

$\frac{9}{2} (γ - 1)$

Q. Let γ denote the ratio of specific heat for an ideal gas. Then choose the correct expression for number of degrees of freedom of a molecule of the same gas.

225​(γ−1)

2γ−13γ−1​

γ−12​

29​(γ−1)

For, E = Total Energy, f = Degree of freedom of molecule, We Know, Cv​= Molar heat capacity at constant volume = (∂T∂U​)v​=2f​R Cp​ = Molar heat capacity at constant pressure =Cv​+R=2(f+2)​R γ = Ratio of specific heats =Cv​Cp​​=ff+2​ ⇒f=γ−12​

Q. Let $γ$ denote the ratio of specific heat for an ideal gas. Then choose the correct expression for number of degrees of freedom of a molecule of the same gas.

$\frac{25}{2} (γ - 1)$

$\frac{3 γ - 1}{2 γ - 1}$

$\frac{2}{γ - 1}$

$\frac{9}{2} (γ - 1)$