The ratio of the specific heats frac{C_p}{C_v | vedclass

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

Question

(C) For $n$ degrees of freedom,the molar heat capacity at constant volume is given by $C_v = \frac{n}{2}R$.From Mayer's relation,we know that $C_p - C

Vedclass · Accepted Answer

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

Vedclass · Answer

(C) For $n$ degrees of freedom,the molar heat capacity at constant volume is given by $C_v = \frac{n}{2}R$.From Mayer's relation,we know that $C_p - C_v = R$,which implies $C_p = C_v + R$.Substituting the value of $C_v$,we get $C_p = \frac{n}{2}R + R = R\left(\frac{n}{2} + 1\right) = R\left(\frac{n+2}{2}\right)$.The ratio of specific heats $\gamma$ is defined as $\gamma = \frac{C_p}{C_v}$.Substituting the expressions for $C_p$ and $C_v$,we get $\gamma = \frac{R(\frac{n+2}{2})}{\frac{n}{2}R} = \frac{n+2}{n} = 1 + \frac{2}{n}$.

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

Similar Questions

The molar specific heat of a monoatomic gas at constant pressure is (Universal gas constant $R = 8.3 \,J \,mol^{-1} \,K^{-1}$)

If $C_p$ and $C_v$ denote the specific heat of nitrogen at constant pressure and constant volume respectively,then

The molar heat capacity of an ideal gas at constant volume is $\alpha R$. If $R$ is the universal gas constant,then the ratio $C_P/C_V$ is equal to ...........

$A$ cylinder of fixed capacity $67.2 \text{ litres}$ contains helium gas at $STP$. The amount of heat needed to raise the temperature of the gas in the cylinder by $20^{\circ} C$ is: (in $\text{ J}$)

What is the significance of the heat capacity ratio $\gamma = \frac{C_{P}}{C_{V}}$ for a gas?

Vedclass Test Series

Exam Paper Generator

Online Exam Module