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Question

Physics Question on Ideal gas equation

A gas has n degrees of freedom. The ratio of specific heat of gas at constant volume to the specific heat of gas at constant pressure will be

A

nn+2\frac{n}{n+2}

B

n+2n\frac{n+2}{n}

C

n2n+2\frac{n}{2n+2}

D

nn−2\frac{n}{n-2}

Answer

nn+2\frac{n}{n+2}

Explanation

Solution

**Ratio of specific heat of gas at constant volume to the specific heat of gas at constant pressure : **

**Specific heat of gas constant volume : **Cv=nR2C_v = \frac{nR}2

Again, **Specific heat of gas at constant pressure : ** Cp=nR2+RC_p = \frac{nR}{2+R}

⇒CvCp⇒ \frac{C_v}{C_p}

= nR2nR2+R\frac{\frac{nR}{2}}{\frac{nR}{2+R}}

= nn+2\frac{n}{n+2}

Hence, the correct option is (A): nn+2\frac{n}{n+2}