JEE Kinetic Theory of Gases PYQs PDF With Video Solutions

Consider a sample of oxygen behaving like an ideal gas. At 300 K, the ratio of root-mean-square (RMS) velocity to the average velocity of the gas molecule would be :
(Molecular weight of oxygen is 32 g mol$$^{-1}$$; $$R = 8.3$$ J K$$^{-1}$$ mol$$^{-1}$$)

The number density of molecules of a gas depends on their distance r from the origin as, $$n(r) = n_0 e^{-\alpha r^4}$$. Then the numer of molecules is proportional to:

In a dilute gas at pressure P and temperature T, the time between successive collision of a molecule varies with T as:

The change in the magnitude of the volume of an ideal gas when a small additional pressure $$\Delta P$$ is applied at a constant temperature, is the same as the change when the temperature is reduced by a small quantity $$\Delta T$$ at constant pressure. The initial temperature and pressure of the gas were 300 K and 2 atm respectively. If $$|\Delta T| = C|\Delta P|$$ then value of C in (K/atm) is __________

Consider a mixture of $$n$$ moles of helium gas and $$2n$$ moles of oxygen gas (molecules taken to be rigid) as an ideal gas. Its $$\frac{C_P}{C_V}$$ value will be:

A gas has $$n$$ degrees of freedom. The ratio of specific heat of gas at constant volume to the specific heat of gas at constant pressure will be

If $$10^{22}$$ gas molecules each of mass $$10^{-26}$$ kg collides with a surface (perpendicular to it) elastically per second over an area 1 m$$^{2}$$ with a speed $$10^{4}$$ m/s, the pressure exerted by the gas molecules will be of the order of:

When 300 J of heat given to an ideal gas with $$C_{p}= \frac{7}{2}R$$ its temperature raises from $$20^{\circ}C$$ to $$50^{\circ}C$$ keeping its volume constant. The millimoles of the gas is (approximately) __ . (R = 8.314 J/mol.K)

According to law of equipartition of energy the molar specific heat of a diatomic gas at constant volume where the molecule has one additional vibrational mode is:-

Which of the following shows the correct relationship between the pressure $$P$$ and density $$\rho$$ of an ideal gas at constant temperature?

A bicycle tyre is filled with air having pressure of $$270$$ kPa at $$27°$$C. The approximate pressure of the air in the tyre when the temperature increases to $$36°$$C is

A sample of 1 mole gas at temperature T is adiabatically expanded to double its volume. If adiabatic constant for the gas is $$\gamma = \frac{3}{2}$$, then the work done by the gas in the process is:

The amount of heat needed to raise the temperature of 4 moles of a rigid diatomic gas from 0 $$^\circ$$C to 50 $$^\circ$$C when no work is done is ($$R$$ is the universal gas constant)

The ratio of vapour densities of two gases at the same temperature is $$\frac{4}{25}$$, then the ratio of r.m.s. velocities will be :

$$N$$ moles of a polyatomic gas $$(f = 6)$$ must be mixed with two moles of a monoatomic gas so that the mixture behaves as a diatomic gas. The value of $$N$$ is:

Following statements are given:
(1) The average kinetic energy of a gas molecule decreases when the temperature is reduced.
(2) The average kinetic energy of a gas molecule increases with increase in pressure at constant temperature.
(3) The average kinetic energy of a gas molecule decreases with increase in volume.
(4) Pressure of a gas increases with increase in temperature at constant volume.
(5) The volume of gas decreases with increase in temperature.
Choose the correct answer from the options given below:

Match the $$\frac{C_p}{C_v}$$ ratio for ideal gases with different type of molecules:
Molecule Type                                    $$C_p/C_v$$
(A) Monoatomic                                 (I) 7/5
(B) Diatomic rigid molecules             (II) 9/7
(C) Diatomic non-rigid molecules      (III) 4/3
(D) Triatomic rigid molecules            (IV) 5/3

For an ideal gas the instantaneous change in pressure $$P$$ with volume $$V$$ is given by the equation $$\frac{dP}{dV} = -aP$$. If $$P = P_0$$ at $$V = 0$$ is the given boundary condition, then the maximum temperature one mole of gas can attain is: (Here $$\mathcal{R}$$ is the gas constant)

Using equipartition of energy, the specific heat (in J kg$$^{-1}$$ K$$^{-1}$$) of Aluminium at high temperature can be estimated to be (atomic weight of Aluminium = 27)

Two moles of helium gas is mixed with three moles of hydrogen molecules (taken to be rigid). What is the molar specific heat of mixture at constant volume? R = 8.3 J/mol K

The r.m.s. speed of oxygen molecules at $$47^\circ$$ is equal to that of the hydrogen molecules kept at ________ $$C^\circ$$. (Mass of oxygen molecule/mass of hydrogen molecule = 32/2)

Sound travels in a mixture of two moles of helium and $$n$$ moles of hydrogen. If rms speed of gas molecules in the mixture is $$\sqrt{2}$$ times the speed of sound, then the value of $$n$$ will be

A closed vessel contains 0.1 mole of a monoatomic ideal gas at 200 K. If 0.05 mole of the same gas at 400 K is added to it, the final equilibrium temperature (in K) of the gas in the vessel will be close to __________

One mole of a monoatomic gas is mixed with three moles of a diatomic gas. The molecular specific heat of mixture at constant volume is $$\frac{\alpha^2}{4}R$$ J mol$$^{-1}$$ K$$^{-1}$$; then the value of $$\alpha$$ will be _____. (Assume that the given diatomic gas has no vibrational mode.)

$$N$$ moles of diatomic gas in a cylinder is at a temperature $$T$$. Heat is supplied to the cylinder such that the temperature remains constant but $$n$$ moles of the diatomic gas get converted into monoatomic gas. The change in the total kinetic energy of the gas is

The internal energy of air in a $$4\,\text{m} \times 4\,\text{m} \times 3\,\text{m}$$ sized room at 1 atmospheric pressure will be _________ $$\times 10^6$$ J.
(Consider air as diatomic molecule)

If one mole of the polyatomic gas is having two vibrational modes and $$\beta$$ is the ratio of molar specific heats for polyatomic gas $$\left(\beta = \frac{C_p}{C_v}\right)$$ then the value of $$\beta$$ is:

To raise the temperature of a certain mass of gas by 50°C at a constant pressure, 160 calories of heat is required. When the same mass of gas is cooled by 100°C at constant volume, 240 calories of heat is released. How many degrees of freedom does each molecule of this gas have (assume gas to be ideal)?

A system consists of two types of gas molecules $$A$$ and $$B$$ having the same number density $$2 \times 10^{25}$$ m$$^{-3}$$. The diameter of $$A$$ and $$B$$ are 10A and 5A respectively. They suffer collisions at room temperature. The ratio of average distance covered by the molecule $$A$$ to that of $$B$$ between two successive collisions is _________ $$\times 10^{-2}$$

A container is divided into two chambers by a partition. The volume of first chamber is 4.5 litre and second chamber is 5.5 litre. The first chamber contain 3.0 moles of gas at pressure 2.0 atm and second chamber contain 4.0 moles of gas at pressure 3.0 atm. After the partition is removed and the mixture attains equilibrium, then, the common equilibrium pressure existing in the mixture is $$x \times 10^{-1}$$ atm. Value of $$x$$ (nearest integer) is ______