Question

The ratio of the specific heats $\frac{C_{P}}{C_{V}}=\gamma$ in terms of degrees of freedom (n) is given by

• A. $\left(1+\frac{n}{3}\right)$
• B. $\left(1+\frac{2}{n}\right)$
• C. $\left(1+\frac{n}{2}\right)$
• D. $\left(1+\frac{1}{n}\right)$

Answer 1

Answer: (B)

The internal energy for 1 mole of gas is given as
$U =\frac{ n }{2} RdT = C _{ v } dT$ where $n$ is degrees of freedom
$C _{ p }- C _{ v }= R$
$Cp =\left(1+\frac{ n }{2}\right) R$
and $\frac{ C _{ p }}{ C _{ v }}=\gamma=\frac{\left(1+\frac{ n }{2}\right) R }{\frac{ n }{2}}=1+\frac{2}{ n }$