Law of Equipartition of Energy and Specific Heat of Gas

A flask contains Hydrogen and Argon in the ratio $2:1$ by mass. The temperature of the mixture is $30°\mathrm{C}$. The ratio of average kinetic energy per molecule of the two gases $\left(\frac{K_{\mathrm{argon}}}{K_{\mathrm{hydrogen}}}\right)$ is: (Given : Atomic Weight of $Ar=39.9$)

Match List I with List II:

Choose the correct answer from the options given below:

The value of$C_P$ for a monoatomic gas is $\frac{5}{2}R$. Then its value of $\gamma$ is (where the symbols have their usual meaning)

To find out the degree of freedom, the expression is 

A vessel contains a non-linear triatomic gas. If $50\%$ of gas dissociate into individual atom, then find new value of degree of freedom by ignoring the vibrational mode and any further dissociation

If water is treated like a solid, each molecule of water at temperature $\mathrm{T}$ will have energy equal to

The translational kinetic energy of $1 \mathrm{g}$ molecule of a gas, at temperature $300 \mathrm{K}$ is $\left(R=8.31 \mathrm{J} {\mathrm{mol}}^{-1} {\mathrm{K}}^{-1}\right)$

A sample of gas consists of ${\mu }_1$ moles of mono-atomic molecules, ${\mu }_2$ moles of diatomic molecules and ${\mu }_3$ moles of linear triatomic molecules. The gas is kept at high temperature. What is the total number of degree of freedom?

Choose the relation between the average kinetic energy and pressure.

If ${\mathrm{C}}_{\mathrm{P}}$ and ${\mathrm{C}}_{\mathrm{v}}$ denote the specific heats of unit mass of nitrogen gas at constant pressure and volume respectively, then:

Total number of degrees of freedom of a rigid diatomic molecule is

Choose the wrong options.

The mean kinetic energy of a vibrating diatomic molecule with two vibrational modes is ($\mathrm{k}=$ Boltzman constant and $\mathrm{T}=$ Temperature)

The average energy per mole of an ideal gas of number of degrees of freedom equal to $n$at temperature$T$ is _____.

When $x$ amount of heat is given to a gas at constant pressure, it performs $\frac{x}{3}$ amount of work. The average number of degrees of freedom per molecule of the gas is:

The average translational kinetic energy of the molecules of a gas will be doubled if at constant :-

Two ideal monatomic gases $\mathrm{A}$ and $\mathrm{B}$ at $27 \mathrm{℃}$ and $37 \mathrm{℃}$ are mixed. The number of moles in gas $\mathrm{A}$ is $2$ and number of moles in gas $\mathrm{B}$ is $3$. What will be the temperature of the mixture?

One mole of a monoatomic gas $\left({\gamma }_1=\frac{5}{3}\right)$ is mixed with one mole of a diatomic gas $\left({\gamma }_2=\frac{7}{5}\right)$. What is the value of $\gamma$ for the mixture?

The kinetic energy of $1\mathrm{kg}$ of oxygen at $300\mathrm{K}$ is $1.356\times {10}^6\mathrm{J}$. Find the kinetic energy of  $4\mathrm{kg}$ of oxygen at $400\mathrm{K}$.

State the law of equipartition  of energy.