Question

if gamma be the ratio of specific heats (cp & cv)
for a perfect gas find the number of degree of freedom of a molecule of gas

Answer 1

cp/cv = y
and
cp - cv = R

cv = R/(y+1)
cp = yR/(y+1)

also for f = degree of freedom
cp = f/2 +1
cv = f/2

f/2 = R/(y+1)

so
f = 2R/(y+1)

hope it helps you
@di

Answer 2

if gamma be the ratio of specific heats (cp & cv)  for a perfect gas then the number of degree of freedom of a molecule of gas is $\frac{2}{Y-1}$

• As we know that, difference of Cp and Cv is equal to R

                     ie,  Cp - Cv = R

• If degree of freedom is represented by f then,    

                          Cp = f/2 +1   and Cv = f/2

$Y=\frac{Cp}{Cv}$

        =$\frac{(f+2)/2}{f/2}$

         =$\frac{f+2}{f}$

Therfore,

$F= \frac{2}{Y-1}$