Kinetic theory of gases practice · Mixed difficulty

The ratio of $\mathrm{C}_{\mathrm{p}}$ and $\mathrm{C}_{\mathrm{v}}$ depends on temperature $\mathrm{T}$ according to relation

A diatomic gas $(\gamma=1.4)$ does $50 {~J}$ of work when it is expanded isobarically. The heat given to the gas in this process is

If the root mean square velocity of hydrogen molecule at a given temperature and pressure is $2 \mathrm{~km} / \mathrm{s}$, the root mean square velocity of oxygen at the same condition in $\mathrm{km} / \mathrm{s}$ is:

Mean free path is inversely proportional to

If the rms velocity of a gas is $v$ ,then

If mass of gas is double and $v_{r m s}$ is half then pressure of gas will be.

At ${0^0}C$ temperature, root mean square speed of which of the following gas will be maximum?

Assertion: For a mixture of non-reactive ideal gases, the total pressure gets contribution from each gas in the mixture.
Reason: In equilibrium, the average kinetic energy of the molecules of different gases will be equal.

Critical temperature of $\mathrm{CO}_2$ is $31.2^{\circ} \mathrm{C}$. In summer, the room temperature is $40^{\circ} \mathrm{C}$.

1 mole of a gas having $\gamma=\frac{7}{5}$ is mixed with 1 mole of a gas having $\gamma=\frac{4}{3}$. What will be the $\gamma$ for the mixture?

The ratio of two specific heats $\frac{{{C_P}}}{{{C_V}}}$ of $CO$ is

For a gas $\gamma = 7/5.$ The gas may probably be

Average K.E. of one single molecule of monoatomic gas is $0.414 \mathrm{eV}$ (of $\perp$ molecule). What will be is temp $=$ ?

Three vessels of equal capacity have gases at
the same temperature and pressure. The first
vessel contains helium (monoatomic), the
second contains fluorine (diatomic) and the
third contains sulfur hexafluoride (polyatomic).
The correct statement, among the following is:

In a dilute gas at pressure $p$ and temperature $T,$ the mean time between successive collisions of a molecule varies with $T$ as

Assertion: In case of collision of gas molecules in a given amount of gas, total kinetic energy is conserved.
Reason: All collisions of the gas molecules in a given amount of gas are elastic.

The number of translatioaonal degrees of freedom of a diatomic gas is

A vessel has $6 \mathrm{~g}$ of hydrogen at pressure $P$ and temperature $500 \mathrm{~K}$. A small hole is made in it so that hydrogen leaks out. How much hydrogen leaks out if the final pressure is $\frac{P}{3}$ and temperature falls to 300 K?

Read the given statements and decide which is/are correct on the basis of kinetic theory of gases
(I) Energy of one molecule at absolute temperature is zero
(II) $r.m.s.$speeds of different gases are same at same temperature
(III) For one gram of all ideal gas kinetic energy is same at same temperature
(IV) For one mole of all ideal gases mean kinetic energy is same at same temperature

At a given temperature the $r.m.s.$ velocity of molecules of the gas is

A certain ideal gas undergoes a polytropic process $p V^n=$ constant such that the molar specific heat during the process is negative. If the ratio of the specific heat of the gas be $\gamma$, then the range of values of $n$ will be

The specific heats, ${C_p}\mathrm{ \,\,and }\,\,{C_V}$ of a gas of diatomic molecules, A are given (in units of $\mathrm{J mo}{\mathrm{l}^{ - 1}}{K^{ - 1}}$) by 29 and 22, respectively. Another gas of diatomic molecules B, has the corresponding values 30 and 21. If they are treated as ideal gases, then

The rate of diffusion is

Pressure of an ideal gas is increased by keeping temperature constant. What is the effect on kinetic energy of molecules?

Given below are two statements :
Statement I : The average momentum of a molecule in a sample of an ideal gas depends on temperature.
Statement II : The rms speed of oxygen molecules in a gas is v. If the temperature is doubled and the oxygen molecules dissociate into oxygen atoms, the rms speed will become $2v.$
In the light of the above statements, choose the correct answer from the options given below:

The $r.m.s.$ speed of gas molecules is given by

At O K which of the following properties of a gas will be zero

The equation of state for $3 \mathrm{~g}$ of oxygen at a pressure $P$ and temperature $T$, when occupying a volume $V$, will be:

An ideal gas in a closed container is slowly heated. As its temperature increases, which of the following statements are true?
A. The mean free path of the molecules decreases.
B. The mean collision time between the molecules decreases.
C. The mean free path remains unchanged.
D. The mean collision time remains unchanged.

The ideal gas equation connecting Pressure (P) Volume (V) and absolute temperature (T) is (Where ${K_B}$ is the Blotzmann Constant and N is the number of molecules)