If a gas has n degrees of freedom,the ratio o | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) The ratio of specific heats $\gamma$ is defined as the ratio of molar specific heat at constant pressure $(C_P)$ to molar specific heat at constan

Vedclass · Accepted Answer

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

Vedclass · Answer

(C) The ratio of specific heats $\gamma$ is defined as the ratio of molar specific heat at constant pressure $(C_P)$ to molar specific heat at constant volume $(C_V)$.According to the law of equipartition of energy,the internal energy per mole is $U = \frac{n}{2}RT$.Thus,$C_V = \frac{dU}{dT} = \frac{n}{2}R$.Using Mayer's relation,$C_P = C_V + R = \frac{n}{2}R + R = R(1 + \frac{n}{2})$.Therefore,$\gamma = \frac{C_P}{C_V} = \frac{R(1 + \frac{n}{2})}{\frac{n}{2}R} = \frac{1 + \frac{n}{2}}{\frac{n}{2}} = \frac{2}{n} + 1 = 1 + \frac{2}{n}$.

If a gas has $n$ degrees of freedom,the ratio of specific heats of the gas is:

Similar Questions

Can we use the degree of freedom to obtain the specific heat capacity of a gas? Explain.

What is the correct relationship between molar specific heat at constant pressure $(C_P)$ and constant volume $(C_V)$? ($R$ is the universal gas constant)

Which of the following formulae is wrong?

For a monoatomic gas,work done at constant pressure is $W$. The heat supplied at constant volume for the same rise in temperature of the gas is

Vedclass Test Series

Exam Paper Generator

Online Exam Module