# The ratio of the specific heats $\frac{C_p}{C_v}= \gamma$ in terms of degrees of freedom (n)  is given by: Option 1) $(1+\frac{1}{n})$ Option 2) $(1+\frac{n}{3})$ Option 3) $(1+\frac{2}{n})$ Option 4) $(1+\frac{n}{2})$

Specific heat capacity at constant pressure -

$C_{p}= C_{v}+R$

$= \left ( \frac{f}{2}+1 \right )R$

- wherein

f = degree of freedom

R= Universal gas constant

Specific heat of gas at constant volume -

$C_{v}= \frac{fR}{2}$

- wherein

f = degree of freedom

R= Universal gas constant

$C_{p}=\left ( \frac{n}{2} +1\right)$

n= degree of freedom

$C_{v}=\frac{nR}{2}$

$\therefore \frac{C_{p}}{C_{v}}=\frac{\left ( \frac{n}{2}+1 \right )R}{\frac{nR}{2}}$

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

$r=1+\frac{2}{n}$

Option 1)

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

Option 2)

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

Option 3)

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

Option 4)

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

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