Molecules of an ideal gas are known to have three translational degrees of freedom and two rotational degrees of freedom. The gas is maintained at a temperature of T. The total internal energy, U of a mole of this gas, and the value of γ(=( C P / C v )) given, respectively, by:

Question

Molecules of an ideal gas are known to have three translational degrees of freedom and two rotational degrees of freedom. The gas is maintained at a temperature of T. The total internal energy, U of a mole of this gas, and the value of &gamma;(=( C P / C v )) given, respectively, by: (A) U =(5/2) RT and &gamma;=(6/5) (B) U =5 RT and &gamma;=(7/5) (C) U =5 RT and &gamma;=(6/5) (D) U =(5/2) RT and &gamma;=(7/5)

Tardigrade Admin · Accepted Answer

Total degree of freedom =3+2=5 U =( nfRT /2) ⇒ (5 RT /2) &gamma; ⇒ (C P / C v ) ⇒ 1+(2/ f ) ⇒ 1+(2/5) ⇒ (7/5)

Q. Molecules of an ideal gas are known to have three translational degrees of freedom and two rotational degrees of freedom. The gas is maintained at a temperature of $T$ . The total internal energy, $U$ of a mole of this gas, and the value of $γ (= \frac{C _{P}}{C _{v}})$ given, respectively, by:

$U = \frac{5}{2} RT$ and $γ = \frac{6}{5}$

$U = 5 RT$ and $γ = \frac{7}{5}$

$U = 5 RT$ and $γ = \frac{6}{5}$

$U = \frac{5}{2} RT$ and $γ = \frac{7}{5}$

Total degree of freedom $= 3 + 2 = 5$
$U = \frac{n f RT}{2} \Rightarrow \frac{5 RT}{2}$
$γ \Rightarrow \frac{C _{P}}{C _{v}} \Rightarrow 1 + \frac{2}{f} \Rightarrow 1 + \frac{2}{5} \Rightarrow \frac{7}{5}$

Q. Molecules of an ideal gas are known to have three translational degrees of freedom and two rotational degrees of freedom. The gas is maintained at a temperature of T. The total internal energy, U of a mole of this gas, and the value of γ(=Cv​CP​​) given, respectively, by:

U=25​RT and γ=56​

U=5RT and γ=57​

U=5RT and γ=56​

U=25​RT and γ=57​