(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

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(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,$\gamma_{\text{mono}} = 1 + \frac{2}{3} = \frac{5}{3} \approx 1.67$.For a diatomic gas,$f = 5$.Therefore,$\gamma_{\text{dia}} = 1 + \frac{2}{5} = \frac{7}{5} = 1.4$.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 $\gamma$.

Class 11 Physics Kinetic Theory of Gases Molar Specific Heat of gas and relation between them (Mayer's formula)

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$Assertion :$ 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.

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A
If both Assertion and Reason are correct and the Reason is a correct explanation of the Assertion.
B
If both Assertion and Reason are correct but Reason is not a correct explanation of the Assertion.
C
If the Assertion is correct but Reason is incorrect.
D
If both the Assertion and Reason are incorrect.

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Kinetic Theory of Gases

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Molar Specific Heat of gas and relation between them (Mayer's formula)

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$306 \ J$ of heat is required to raise the temperature of $2 \ moles$ of an ideal gas at constant pressure from $25^{\circ} C$ to $35^{\circ} C$. The amount of heat required to raise the temperature of the same gas through the same range at constant volume is (in $J$)

DifficultAP EAMCET 2020

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Explain the difference between the expressions $C_P - C_V = R$,$C_P - C_V = \frac{R}{J}$,and $C_P - C_V = \frac{r}{J}$.

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For a gas,the value of $\frac{R}{C_v} = 0.4$. What is the nature of the gas? ($R$ is the universal gas constant)

EasyAP EAMCET 2019

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The molar specific heat at constant pressure of an ideal gas is $\frac{7}{2} R$. The gas is made up of molecules which are ( $R$ is the universal gas constant)

MediumMHT CET 2022

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$Assertion :$ 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

$306 \ J$ of heat is required to raise the temperature of $2 \ moles$ of an ideal gas at constant pressure from $25^{\circ} C$ to $35^{\circ} C$. The amount of heat required to raise the temperature of the same gas through the same range at constant volume is (in $J$)

Explain the difference between the expressions $C_P - C_V = R$,$C_P - C_V = \frac{R}{J}$,and $C_P - C_V = \frac{r}{J}$.

The specific heat of argon at constant pressure and constant volume are $C_p$ and $C_v$ respectively. Its density $\rho$ at $N.T.P.$ will be: [Where $P$ and $T$ are pressure and temperature respectively at $N.T.P.$]

For a gas,the value of $\frac{R}{C_v} = 0.4$. What is the nature of the gas? ($R$ is the universal gas constant)

The molar specific heat at constant pressure of an ideal gas is $\frac{7}{2} R$. The gas is made up of molecules which are ( $R$ is the universal gas constant)

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$Assertion :$ 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.