Kinetic theory of gases practice · Mixed difficulty

If at the same temperature and pressure, the densities of two diatomic gases are $d_1$ and $d_2$, respectively. The ratio of mean kinetic energy per molecule of gases will be

The absolute temperature of a gas is increases 3 times. The root mean square velocity of the moelcules will be

Assertion: The root mean square and most probable speeds of the molecules in a gas are the same
Reason: The Maxwell's distribution for the speed of molecules in a gas is symmetrical.

For a gas at a temperature $\mathrm{T}$ the root mean square velocity $\mathrm{V}_{\mathrm{rms}}$ and the most probable speed $V_{m p}$, and the average speed $V_{a v}$ obey the relationship -

In a vertical open vessel an ideal gas is filled and it is enclosed by a piston of mass $4 \mathrm{~kg}$ and cross-section area is $2 \mathrm{~cm}^2$ then find out pressure applied by gas on piston in equilibrium.

An ideal gas is allowed to expands from volume $V$ to $2 V$ according to the law $V P^2=$ Constant. If initial temperature of the gas is $T$ then its final temperature will be

The volume of vessel $A$ is twice the volume of another vessel $B$, and both of them are filled with the same gas. If the gas in $A$ is at twice the temperature and twice the pressure in comparison to the gas in $B$, then the ratio of the gas molecules in $A$ to that of $B$

Assertion: Equal masses of helium and oxygen gases are given equal quantities of heat. There will be a greater rise in the temperature of helium compared to that of oxygen.
Reason: The molecular weight of oxygen is more than the molecular weight of helium.

If the molecular weight of two gases are ${M_1}$ and ${M_2}$, then at a temperature the ratio of root mean square velocity ${v_1}$ and ${v_2}$ will be

Which statements are correct about degrees of freedom?
(A) A molecule with $n$ degrees of freedom has $n^2$ different ways of storing energy.
(B) Each degree of freedom is associated with $\frac{1}{2} R T$ average energy per mole.
(C) A monatomic gas molecule has 1 rotational degree of freedom whereas diatomic molecule has 2 rotational degrees of freedom.
(D) $\mathrm{CH}_4$ has a total of 6 degrees of freedom.
Choose the correct answer from the option given below:

A gas is taken through a number of thermodynamic states. What happens to its specific heat?

Assertion(A): If initial and final volumes are equal, then work done by gas is zero.

Reason(R): In isochoric process, initial and final volumes are equal and work done by gas is zero.

In the absence of intermolecular forces of attraction, the observed pressure $p$ will be

The rms speed of an ideal diatomic gas at temperature $T$ is $V$. When gas dissociates into atoms then its new rms speed becomes double. The temperature at which the gas dissociated into atoms are:

According to the kinetic theory of gases, the temperature of a gas is a measure of average

Two moles of an ideal gas with $\frac{{{C_p}}}{{{C_V}}} = \frac{5}{3}$ are mixed with 3 mol of another ideal gas with $\frac{{{C_p}}}{{{C_V}}} = \frac{4}{3}.$ The value of $\frac{{{C_p}}}{{{C_V}}}$ for the mixture is

The relation between rms velocity, $v_{\text {rms}}$ and the most probable velocity, $v_{{mp}}$ of a gas is

Statement-I: Moon has no atmosphere
Statement-II: The root mean square velocity of air molecules on moon is greater than the escape velocity of air molecules on moon.

Assertion: Absolute zero temperature is not the temperature of zero energy
Reason: Only the translational kinetic energy of the molecules is represented by temperature.

If the degree of freedom of a gas are $f,$ then the ratio of two specific heats ${C_P}/{C_V}$ is given by