Kinetic Theory

At which temperature the r.m.s. velocity of a hydrogen molecule equal to that of an oxygen molecule at \(47^{\circ} \mathrm{C}\) ?

Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R.
Assertion A: If the average kinetic energy of \({\mathrm{H}}_{2}\) and \({\mathrm{O}}_{2}\) molecules, kept in two different sized containers are same, then their temperatures will be same.
Reason R: The r.m.s. speed of \({\mathrm{H}}_{2}\) and \({\mathrm{O}}_{2}\) molecules are same at same temperature.
Choose the correct answer from the options given below.

[04 April, 2026 (Shift-II)]

An ideal gas undergoes a process maintaining relation between pressure (P) and Volume (V) as \(P={P}_{0}{\left(1+{\left(\frac{{V}_{0}}{V}\right)}^{2}\right)}^{-1}\) where \({P}_{0}\) and \({V}_{0}\) are constants. If two samples A and B (two moles each) with initial volumes \({V}_{0}\) and \(3{V}_{0}\) respectively undergo above mentioned process and attain same pressure, then the difference at the temperatures of these samples \({T}_{B}-{T}_{A}\)_____.(R= gas constant)

[04 April, 2026 (Shift-I)]

If the root mean square velocity of hydrogen molecule at a given temperature and pressure is \(2 km / s\), the root mean square velocity of oxygen at the same condition in \(km / s\) is:EndFragment

[JEE Main 2024, 01 Feb (Shift 2)]

If the root mean square velocity of hydrogen molecule at a given temperature and pressure is \(2 km / s\), the root mean square velocity of oxygen at the same condition in \(km / s\) is:EndFragment

[JEE Main 2024, 01 Feb (Shift 2)]

For a diatomic gas, if \({\gamma }_{1}=\left(\frac{Cp}{Cv}\right)\) for rigid molecules and \({\gamma }_{2}=\left(\frac{Cp}{Cv}\right)\) for another diatomic molecules, but also having vibrational modes. Then, which one of the following options is correct ? (Cp and Cv are specific heats of the gas at constant pressure and volume)

[JEE Main 2025, 22 Jan (Shift 2)]

Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R):

Assertion (A): Change in internal energy of a system containing n mole of ideal gas can be written as \(∆U=n{C}_{v}\left({T}_{f}-{T}_{i}\right)=\frac{nR}{\gamma -1}\left({T}_{f}-{T}_{i}\right),\) where \(\gamma =\frac{{C}_{p}}{C},{T}_{i}\)\(=\text{ initial temperature, }{T}_{f}=\text{ final temperature. }\)
Reason (R): Relation between degree of freedom \(f\text{ and }\gamma \left(={C}_{p}/{C}_{v}\right)\) \(\text{ is }\left(\gamma =1+\frac{2}{f}\right)\text{. }\)

Choose the correct answer from the options given below:

[JEE Main 2026, 5 Apr (Shift 1)]

If 2 mole of an ideal monoatomic gas at temperature T, is mixed with 6 mole of another ideal monoatomic gas at temperature 2T then the temperature of mixture is:

[JEE Main 2026, 6 Apr (Shift 2)]

For a diatomic gas:

• Let \({\gamma }_{1}=\frac{{C}_{p}}{{C}_{v}}\) for a rigid molecule (without vibrational modes).
• Let \({\gamma }_{2}=\frac{{C}_{p}}{{C}_{v}}\)​​ for a diatomic molecule with vibrational modes included.

Determine the relationship between \({\gamma }_{1}\)​ and \({\gamma }_{2}\)​.

(Shift II Memory Based)​

For a diatomic gas, if \({\gamma }_{1}=\left(\frac{Cp}{Cv}\right)\) for rigid molecules and \({\gamma }_{2}=\left(\frac{Cp}{Cv}\right)\) for another diatomic molecules, but also having vibrational modes. Then, which one of the following options is correct ? (Cp and Cv are specific heats of the gas at constant pressure and volume)

A mixture of one mole of monoatomic gas and one mole of a diatomic gas (rigid) are kept at room temperature \(\left(27^\circ \mathrm{C}\right)\). The ratio of specific heat of gases at constant volume respectively is:

If the root mean square velocity of hydrogen molecule at a given temperature and pressure is \(2 km / s\), the root mean square velocity of oxygen at the same condition in \(km / s\) is:EndFragment

For a diatomic gas, if \({\gamma }_{1}=\left(\frac{Cp}{Cv}\right)\) for rigid molecules and \({\gamma }_{2}=\left(\frac{Cp}{Cv}\right)\) for another diatomic molecules, but also having vibrational modes. Then, which one of the following options is correct ? (Cp and Cv are specific heats of the gas at constant pressure and volume)

[JEE Main 2025, 22 Jan (Shift 2)]

The translational kinetic energy of molecules of \(50 \mathrm{~g} \quad\mathrm{of}\quad \mathrm{CO}_2\) gas at \(17^{\circ} \mathrm{C}\) is:

(Shift - II Memory Based)

The total kinetic energy of 1 mole of oxygen at \(27^{\circ} C\) is : [Use universal gas constant \(( R )=8.31 \ J /\) mole K]

[JEE Main 2024, 27 Jan (Shift 2)]

The total kinetic energy of 1 mole of oxygen at \(27^{\circ} C\) is : [Use universal gas constant \(( R )=8.31 \ J /\) mole K]

[JEE Main 2024, 27 Jan (Shift 2)]

The helium and argon are put in the flask at the same room temperature ( \(300K\) ). The ratio of average kinetic energies (per molecule) of helium and argon is : (Given : Molar mass of helium \(=4\mathrm{g}/\mathrm{mol}\), Molar mass of argon \(=40\mathrm{g}/\mathrm{mol}\) )

Heat is supplied to a diatomic gas at constant pressure. Then the ratio of \(∆Q:∆U:∆W\) is ________.

[JEE Main 2026, 2 Apr (Shift 1)]

There are two vessels filled with an ideal gas where volume of one is double the volume of other. The large vessel contains the gas at 8 kPa at 1000 K while the smaller vessel contains the gas at 7 kPa at 500 K. If the vessels are connected to each other by a thin tube allowing the gas to flow and the temperature of both vessels is maintained at 600 K, at steady state the pressure in the vessels will be (in kPa).

[JEE Main 2025, 4 Apr (Shift 2)]

One mole of diatomic gas having rotational modes only is kept in a cylinder with a piston system. The cross-section area of the cylinder is \(4c{m}^{2}\). The gas is heated slowly to raise the temperature by \(1.2^\circ C\) during which the piston moves by 25 mm. The amount of heat supplied to the gas is __________ J.
(Atmospheric pressure \(=100kPa,R=8.3J/mol.K\) ) (Neglect mass of the piston)

[JEE Main 2026, 8 Apr (Shift 2)]

The mean free path and the average speed of oxygen molecules at \(300K\) and \(1\) atm are \(3\times {10}^{-7}\mathrm{m}\) and \(600\mathrm{m}/\mathrm{s}\), respectively. Find the frequency of its collisions.

[JEE Main 2025, 4 Apr (Shift 1)]

The translational kinetic energy of molecules of \(50 \mathrm{~g} \quad\mathrm{of}\quad \mathrm{CO}_2\) gas at \(17^{\circ} \mathrm{C}\) is:

(Shift - II Memory Based)

The total kinetic energy of 1 mole of oxygen at \(27^{\circ} C\) is : [Use universal gas constant \(( R )=8.31 \ J /\) mole K]

If the root mean square velocity of hydrogen molecule at a given temperature and pressure is \(2 km / s\), the root mean square velocity of oxygen at the same condition in \(km / s\) is:

StartFragment [1-Feb.-2024_JEE Main (Shift-II)]EndFragment

A mixture of carbon dioxide and oxygen has volume \(8310c{m}^{3}\), temperature 300 K , pressure 100 kPa and mass 13.2 g . The number of moles of carbon dioxide and oxygen gases in the mixture respectively are _________
(Assume both carbon dioxide and oxygen gases behave like ideal gases) \([R=8.31J/mol.K]\)

[02 April, 2026 (Shift-2)]

One gas of \({n}_{1}\)mole of molecules at temperature \({T}_{1}\), volume \({V}_{1}\), and pressure \({P}_{1}\), and another gas of \({n}_{2}\) mole of molecules at temperature \({T}_{2}\), volume \({V}_{2}\), and pressure\({P}_{2}\), are mixed resulting in pressure P and volume V of the mixture. the temperature of the mixture is ______.

[04 April, 2026 (Shift-I)]

The helium and argon are put in the flask at the same room temperature ( \(300K\) ). The ratio of average kinetic energies (per molecule) of helium and argon is :
(Given : Molar mass of helium \(=4\mathrm{g}/\mathrm{mol}\), Molar mass of argon \(=40\mathrm{g}/\mathrm{mol}\) )

[JEE Main 2025, 7 Apr (Shift 2)]

For a diatomic gas, if \({\gamma }_{1}=\left(\frac{Cp}{Cv}\right)\) for rigid molecules and \({\gamma }_{2}=\left(\frac{Cp}{Cv}\right)\) for another diatomic molecules, but also having vibrational modes. Then, which one of the following options is correct ? (Cp and Cv are specific heats of the gas at constant pressure and volume)

[JEE Main 2025, 22 Jan (Shift 2)]

For a diatomic gas:

• Let \({\gamma }_{1}=\frac{{C}_{p}}{{C}_{v}}\) for a rigid molecule (without vibrational modes).
• Let \({\gamma }_{2}=\frac{{C}_{p}}{{C}_{v}}\)​​ for a diatomic molecule with vibrational modes included.

Determine the relationship between \({\gamma }_{1}\)​ and \({\gamma }_{2}\)​.

(Shift II Memory Based)​

A monatomic gas is heated at constant pressure, with 0.5 moles of the gas receiving 500 J of heat. The initial temperature of the gas is 27°C. Determine the change in temperature (\(\Delta T\)) and the work done (\(W\)) by the gas.

Given below are two statements:
Statement I: In a diatomic molecule, the rotational energy at a given temperature obeys Maxwell's distribution.
Statement II: In a diatomic molecule, the rotational energy at a given temperature equals the translational kinetic energy for each molecule.
In the light of the above statements, choose the correct answer from the options given below:

[JEE Main 2021, 25 Feb (Shift 2)]

The average thermal energy for a mono-atomic gas is : (k_B is Boltzmann constant and \( \mathrm{T} \), absolute temperature)

The number of air molecules per cm³ increased from 3 × 10¹⁹ to 12 × 10¹⁹. The ratio of collision frequency of air molecules before and after the increase in number respectively is:

[JEE Main 2023, 6 Apr (Shift 1)]

At temperature 300 K, the rms speed of oxygen molecules is \(\sqrt{\frac{\alpha +5}{\alpha }}\) times to that of its average speed in the gas. Then, the value of a will be \(\text{ (use }\pi =\frac{22}{7}\text{ ) }\)

The volume \(V\) of an enclosure contains a mixture of three gases, 16g of oxygen, 28g of nitrogen and 44g of carbon dioxide at absolute temperature T. Consider \(R\) as universal gas constant. The pressure of the mixture of gases is:

[JEE Main 2021, 16 Mar (Shift 1)]

The average kinetic energy of an ideal gas molecule

[JEE Main 2023, 1 Feb (Shift 1)]

Given below are two statements:

Statement I: The temperature of a gas is - \( 73^{\circ} \mathrm{C} \). When the gas is heated to \( 537^{\circ} \mathrm{C} \), the root

mean square speed of the molecules is doubled.

Statement II: The product of pressure and volume of an ideal gas will be equal to translational kinetic energy of the molecules.

In the light of the above statements, choose the Correct answer from the options given below:

[JEE Main 2023, 24 Jan (Shift 1)]

The average kinetic energy of a molecule of the gas is

[JEE Main 2023, 1 Feb (Shift 1)]

Consider a mixture of gas molecule of types \(A, B\) and \(C\) having masses \(m_A

A gas mixture consists of 2 moles of oxygen and 4 moles of neon at temperature T. Neglecting all vibrational modes, the total internal energy of the system will be:

[JEE Main 2023, 10 Apr (Shift 2)]

The correct relation between \(\gamma=\frac{C_p}{C_v}\) and temperature \(T\) is:

[JEE Main 2023,31 Jan (Shift 1)]

The root mean square speed of molecules of nitrogen gas at \(27^{\circ} C\) is approximately:
(Given mass of a nitrogen molecule \(-4.6 \times 10^{-26} kg\) and take Boltzmann constant \(k_B=1.4 \times 10^{-23} J^{-1}\) )

[JEE Main 2023, 11 Apr (Shift 2)]

The volume \(V\) of an enclosure contains a mixture of three gases, 16g of oxygen, 28g of nitrogen and 44g of carbon dioxide at absolute temperature T. Consider \(R\) as universal gas constant. The pressure of the mixture of gases is:

What will be the average value of energy for a monoatomic gas in thermal equilibrium at a temperature \(\mathrm{T}\) ?

[JEE Main 2021, 22 Jul (Shift 2)]

The ratio of speed of sound in hydrogen gas to the speed of sound in oxygen gas at the same temperature is:

[JEE Main 2023, 6 Apr (Shift 2)]

If the r.m.s. speed of chlorine molecule is \(490 m / s\) at \(27^{\circ} C\), the r.m.s. speed of argon molecules at the same temperature will be (Atomic mass of argon \(=39.9 u\), molecular mass of chlorine \(=70.9 u )\)

[JEE Main 2023, 12 Apr (Shift 1)]

The root mean square speed of molecules of nitrogen gas at \(27^{\circ} C\) is approximately:
(Given mass of a nitrogen molecule \(-4.6 \times 10^{-26} kg\) and take Boltzmann constant \(k_B=1.4 \times 10^{-23} JK^{-1}\) )

[JEE Main 2023, 11 Apr (Shift 2)]

On the basis of kinetic theory of gases, the gas exerts pressure because its molecules:

The number of molecules in one litre of an ideal gas at \(300 K\) and 2 atmospheric pressure with mean kinetic energy \(2 \times 10^{-9} J\) per molecule is:

The rms speed of an oxygen molecule in a vessel at particular temperature is \(\left(1+\frac{5}{x}\right)^{\frac{1}{2}} v\), where \(v\) is the average speed of the molecule. The value of \(x\) will be: (Take \(\pi=\frac{22}{7}\))

[JEE Main 2023, 13 Apr (Shift 1)]

Consider a mixture of gas molecule of types \(A, B\) and \(C\) having masses \(m_A

[JEE Main 2021, 20 July (Shift 1)]

The pressure (P) and temperature (T) relationship of an ideal gas obeys the equation PT² = constant. The volume expansion coefficient of the gas will be:

A closed container contains a homogeneous mixture of two moles of an ideal monoatomic gas \((\gamma=5 / 3)\) and one mole of an ideal diatomic gas \((\gamma=7 / 5)\). Here, \(\gamma\) is the ratio of the specific heats at constant pressure and constant volume of an ideal gas. The gas mixture does a work of 66 Joule when heated at constant pressure. The change in its internal energy is ________ Joules.

[JEE Advanced 2023]

Three vessels of equal volume contain gases at the same temperature and pressure. The first vessel contains neon (monoatomic), the second contains chlorine (diatomic) and third contains uranium hexafluoride (polyatomic). Arrange these on the basis of their root mean square speed \(\left(v_{r m s}\right)\) and choose the correct answer from the options given below:

[JEE Main 2023, 11 Apr (Shift 1)]

A flask contains hydrogen and oxygen in the ratio of \(2: 1\) by mass at a temperature \(27^{\circ} C\). The ratio of average kinetic energy per molecule of hydrogen and oxygen respectively is:

[JEE Main 2023, 30 Jan (Shift 2)]

The temperature of an ideal gas is increased from \(200 K\) to \(800 K\). If r.m.s. speed of gas at \(200 K\) is \(v_0\), then, r.m.s. speed of the gas at \(800 K\) will be:

[JEE Main 2023, 6 Apr (Shift 2)]

Two ideal polyatomic gases at temperatures \(\boldsymbol{T}_{\mathbf{1}}\) and \(\boldsymbol{T}_{\mathbf{2}}\) are mixed so that there is no loss of energy. If \(\boldsymbol{F}_1\) and \(\boldsymbol{F}_2, \boldsymbol{m}_1\) and \(\boldsymbol{m}_2, \boldsymbol{n}_1\) and \(\boldsymbol{n}_2\) be the degrees of freedom, masses, number of molecules of the first and second gas respectively, the temperature of mixture of these two gases is:

[JEE Main 2021, 17 Mar (Shift 1)]

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 gas molecule would be:
(Molecular weight of oxygen is \(32 g / mol ; R=8.3 JK ^{-1}\) \(\left.mol ^{-1}\right)\)

[JEE Main 2021, 18 Mar (Shift 2)]

A flask contains hydrogen and argon in the ratio 2 : 1 by mass. The temperature of the mixture is 30°C. The ratio of average kinetic energy per molecule of the two gases

(K_argon / K_hydrogen) is: (Given: Atomic Weight of Ar = 39.9)

[JEE Main 2023, 15 Apr (Shift 1)]

At temperature \(300 K\), the rms speed of oxygen molecules is \(\sqrt{\frac{\alpha+5}{\alpha}}\) times to that of its average speed in the gas. Then, the value of \(\alpha\) will be (use \(\pi=\frac{22}{7}\) )

[JEE Main 2023, 13 Apr (Shift 1)]

A polyatomic ideal gas has 24 vibrational modes. What is the value of \(\gamma\)?

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

[JEE Main 2023, 29 Jan (Shift 1)]

If the rms speed of oxygen molecules at \(0^{\circ} C\) is \(160 \ m/s\), find the rms speed of hydrogen molecules at \(0^{\circ} C\).

[JEE Main 2021, 27 Aug (Shift 2)]

The mean free path of molecules of a certain gas at STP is \(1500 d\), where \(d\) is the diameter of the gas molecules. While maintaining the standard pressure, the mean free path of the molecules at \(373 K\) is approximately:

[JEE Main 2023, 13 Apr (Shift 2)]

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:

[JEE Main 2023, 25 June (Shift 2)]