Assertion : The ratio of frac{C_p}{C_v} for a | vedclass

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

Question

(A) If $f$ is the degree of freedom,then the ratio $\gamma = \frac{C_p}{C_v}$ is given by $\gamma = 1 + \frac{2}{f}$.For a monoatomic gas,$f = 3$.Ther

Vedclass · Accepted Answer

If both Assertion and Reason are correct and the Reason is a correct explanation of the Assertion.

Vedclass · Answer

(A) If $f$ is the degree of freedom,then the ratio $\gamma = \frac{C_p}{C_v}$ is given by $\gamma = 1 + \frac{2}{f}$.For a monoatomic gas,$f = 3$.Therefore,$\gamma_{	ext{mono}} = 1 + \frac{2}{3} = \frac{5}{3} \approx 1.67$.For a diatomic gas,$f = 5$.Therefore,$\gamma_{	ext{dia}} = 1 + \frac{2}{5} = \frac{7}{5} = 1.4$.Since $1.4 The reason is correct because the degree of freedom $f$ is higher for diatomic molecules $(f=5)$ than for monoatomic atoms $(f=3)$,which leads to a smaller value of $\gamma$.

$Assertion :$ The ratio of $\frac{C_p}{C_v}$ for an ideal diatomic gas is less than that for an ideal monoatomic gas (where $C_p$ and $C_v$ have usual meaning).
$Reason :$ The atoms of a monoatomic gas have less degrees of freedom as compared to molecules of the diatomic gas.

Similar Questions

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

What amount of heat (in $J$) must be supplied to $2.0 \times 10^{-2} \; kg$ of nitrogen (at room temperature) to raise its temperature by $45 \; ^{\circ}C$ at constant pressure? (Molecular mass of $N_{2} = 28; R = 8.3 \; J \; mol^{-1} K^{-1}$.)

The specific heat at constant pressure $(C_P)$ is greater than the specific heat at constant volume $(C_V)$ for the same gas because:

Write the value of $\gamma$ for a polyatomic gas.

The specific heat capacity of a monatomic gas at constant volume is $x \%$ of its specific heat capacity at constant pressure. Then $x=$

Vedclass Test Series

Exam Paper Generator

Online Exam Module

$Assertion :$ The ratio of $\frac{C_p}{C_v}$ for an ideal diatomic gas is less than that for an ideal monoatomic gas (where $C_p$ and $C_v$ have usual meaning).$Reason :$ The atoms of a monoatomic gas have less degrees of freedom as compared to molecules of the diatomic gas.