The ratio of the specific heats (CP/CV)=γ in terms of degrees of freedom (n) is given by

Question

The ratio of the specific heats (CP/CV)=&gamma; in terms of degrees of freedom (n) is given by (A) (1+(n/3)) (B) (1+(2/n)) (C) (1+(n/2)) (D) (1+(1/n))

Tardigrade Admin · Accepted Answer

The internal energy for 1 mole of gas is given as U =( n /2) RdT = C v dT where n is degrees of freedom C p - C v = R Cp =(1+( n /2)) R and ( C p / C v )=&gamma;=((1+( n /2)) R /( n )2)=1+(2/ n )

Q. The ratio of the specific heats $\frac{C _{P}}{C _{V}} = γ$ in terms of degrees of freedom (n) is given by

$(1 + \frac{n}{3})$

$(1 + \frac{2}{n})$

$(1 + \frac{n}{2})$

$(1 + \frac{1}{n})$

The internal energy for 1 mole of gas is given as
$U = \frac{n}{2} R d T = C_{v} d T$ where $n$ is degrees of freedom
$C_{p} - C_{v} = R$
$Cp = (1 + \frac{n}{2}) R$
and $\frac{C _{p}}{C _{v}} = γ = \frac{( 1 + \frac{n}{2} ) R}{\frac{n}{2}} = 1 + \frac{2}{n}$

Q. The ratio of the specific heats CV​CP​​=γ in terms of degrees of freedom (n) is given by

(1+3n​)

(1+n2​)

(1+2n​)

(1+n1​)