If the ratio of specific heats of a gas at co | vedclass

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

Question

(B) The ratio of specific heats $\gamma$ is defined as $\gamma = \frac{C_p}{C_v}$.For an ideal gas,the molar specific heat at constant volume is $C_v

Vedclass · Accepted Answer

$\frac{2}{\gamma-1}$

Vedclass · Answer

(B) The ratio of specific heats $\gamma$ is defined as $\gamma = \frac{C_p}{C_v}$.For an ideal gas,the molar specific heat at constant volume is $C_v = \frac{f}{2}R$,where $f$ is the number of degrees of freedom.The molar specific heat at constant pressure is $C_p = C_v + R = (\frac{f}{2} + 1)R$.Therefore,$\gamma = \frac{C_p}{C_v} = \frac{(\frac{f}{2} + 1)R}{\frac{f}{2}R} = \frac{\frac{f+2}{2}}{\frac{f}{2}} = \frac{f+2}{f} = 1 + \frac{2}{f}$.Rearranging this equation to solve for $f$:$\gamma - 1 = \frac{2}{f}$.$f = \frac{2}{\gamma - 1}$.Thus,the correct option is $B$.

If the ratio of specific heats of a gas at constant pressure and at constant volume is $\gamma$,then the number of degrees of freedom of the rigid molecules of the gas is

Similar Questions

The specific heats,$C_P$ and $C_V$ of a gas of diatomic molecules,$A$,are given (in units of $J\, mol^{-1}\, K^{-1}$) by $29$ and $22$,respectively. Another gas of diatomic molecules,$B$,has the corresponding values $30$ and $21$. If they are treated as ideal gases,then:

The internal energy $(U)$,pressure $(P)$,and volume $(V)$ of an ideal gas are related as $U = 3PV + 4$. The gas is:

The translational degrees of freedom $(f_t)$ and rotational degrees of freedom $(f_r)$ of a $CH_4$ molecule are:

The ratio of specific heats of a gas is $\frac{9}{7}$. The number of degrees of freedom of the gas molecules for translational motion is:

$A$ polyatomic ideal gas has $24$ vibrational modes. What is the value of $\gamma$ ?

Vedclass Test Series

Exam Paper Generator

Online Exam Module