Law of Equipartition of Energy

An oxygen molecule has degrees of freedom at room temperature.

The internal energy of $10 \mathrm{g}$ of nitrogen at $N.T.P.$ is about, $(R=8.31 \mathrm{J} {\mathrm{K}}^{-1})$. 

If $\mathrm{\alpha }$ moles of a monoatomic gas are mixed with $\mathrm{\beta }$ moles of a polyatomic gas and mixture behaves like diatomic gas, then [neglect the vibrational mode of freedom]

If hydrogen gas is heated to a very high temperature, then the fraction of energy possessed by gas molecules correspond to rotational motion

Three perfect gases at absolute temperatures $T_1,T_2$  and $T_3$ are mixed. If number of molecules of the gases are $n_1, n_2$ and $n_3$ respectively then temperature of mixture will be (assume no loss of energy)

A box of negligible mass containing $2$ moles of an ideal gas of molar mass $M$ and adiabatic exponent $\gamma$ moves with constant speed $v$ on a smooth horizontal surface. If the box suddenly stops, then change in temperature of gas will be

When one mole of monatomic gas is mixed with one mole of a diatomic gas, then the equivalent value of $\gamma$ for the mixture will be (vibration mode neglected)

$14 \mathrm{g}$ of $\mathrm{CO}$ at $27°\mathrm{C}$ is mixed with $16 \mathrm{g}$ of ${\mathrm{O}}_2$ at $47°\mathrm{C}.$ The temperature of mixture is (vibration mode neglected)

A mixture of ideal gas has $2$ moles of $\mathrm{He}$, $4$ moles of ${\mathrm{O}}_2$ and $1$ mole of ${\mathrm{O}}_3$ at absolute temperature $T.$ The internal energy of the mixture is

Nitrogen gas is filled in an insulated container. If $\mathrm{\alpha }$ fraction of moles dissociates without exchange of any energy, then the fractional change in its temperature is

If a gas has $\text{'}f\text{'}$ degree of freedom, the ratio of the specific heats of the gases $\frac{C_p}{C_v}$ is

An ant is moving on a plane horizontal surface. The number of degrees of freedom of the ant will be

For a _____ gas having vibrational mode, $\frac{C_P}{C_V}=\frac{9}{7}$.

The translational _____ energy of an ideal gas is $E= \frac{3}{2} k_{B}NT,$ where $N$ is a total number of molecules.

Each vibrational mode gives _____ degrees of freedom.(one/two/three)

Define: degrees of freedom.

A container has $N$ molecules at absolute temperature $T$. If the number of molecules is doubled but kinetic energy in box remains the same as before, the absolute temperature of the gas is