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Kinetic Theory of Gases — JEE Main & Advanced Physics PYQs

383 previous year questions from Kinetic Theory of Gases with answers and solutions. Numbered list, year tags, and one-tap solutions — built for serious JEE / NEET practice.

383 questionsPhysicsSolutions on every page
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 :

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Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R Statement I: Change in internal energy of a system containing n mole of ideal g

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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 H₂ and O₂ molecules, kept in two

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One gas of n₁ mole of molecules at temperature T₁ , volume V₁ , and pressure P₁ , and another gas of n₂ mole of molecules at temperature T₂ , volume V₂ , and pressure P₂ , are mixe

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A mixture of carbon dioxide and oxygen has volume 8310 cm ^3 , temperature 300 K, pressure 100 kPa and mass 13.2 g. The number of moles of carbon dioxide and oxygen gases in the mi

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The mean free path of a molecule of diameter 5 10⁻¹⁰ ~m at the temperature 41^ C and pressure 1.38 10⁵ ~Pa , is given as _ _ _ _ m. (Given k_ B =1.38 10⁻²³ ~J / K ).

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A gas of certain mass filled in a closed cylinder at a pressure of 3.23 kPa has temperature 50^ C . The gas is now heated to double its temperature. The modified pressure is _ _ _

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Consider two boxes containing ideal gases A and B such that their temperatures, pressures and number densities are same. The molecular size of A is half of that of B and mass of mo

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The volume of an ideal gas increases 8 times and temperature becomes (1 / 4)^ th of initial temperature during a reversible change. If there is no exchange of heat in this process

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A cylindrical tube A B of length l , closed at both ends contains an ideal gas of 1 mol having molecular weight M . The tube is rotated in a horizontal plane with constant angular

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

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The helium and argon are put in the flask at the same room temperature ( 300 K). The ratio of average kinetic energies (per molecule) of helium and argon is : (Give : Molar mass of

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Match the List-I with List-II array |l|l|l|l| & List-I & & List-II A. & Triatomic rigid gas & I. & C _ P C _ V = 5 3 B. & array l Diatomic non-rigid gas array & II. & C _ P C _ V =

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The mean free path and the average speed of oxygen molecules at 300 K and 1 atm are 3 10⁻⁷ ~m and 600 ~m / s respectively. Find the frequency of its collisions.

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_ A is the specific heat ratio of monoatomic gas A having 3 translational degrees of freedom. _B is the specific heat ratio of polyatomic gas B having 3 translational, 3 rotational

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The kinetic energy of translation of the molecules in 50 g of CO ₂ gas at 17^ C is

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

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For a particular ideal gas which of the following graphs represents the variation of mean squared velocity of the gas molecules with temperature?

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The temperature of a gas is -78^ C and the average translational kinetic energy of its molecules is K . The temperature at which the average translational kinetic energy of the mol

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Given below are two statements : Statement (I) : The mean free path of gas molecules is inversely proportional to square of molecular diameter. Statement (II) : Average kinetic ene

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A mixture of one mole of monoatomic gas and one mole of a diatomic gas (rigid) are kept at room temperature (27^ C ) . The ratio of specific heat of gases at constant volume respec

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Energy of 10 non rigid diatomic molecules at temperature T is :

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A sample contains mixture of helium and oxygen gas. The ratio of root mean square speed of helium and oxygen in the sample, is:

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The specific heat at constant pressure of a real gas obeying P V^2=R T equation is:

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During an adiabatic process, if the pressure of a gas is found to be proportional to the cube of its absolute temperature, then the ratio of C_ P C _ V for the gas is :

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If n is the number density and d is the diameter of the molecule, then the average distance covered by a molecule between two successive collisions (i.e. mean free path) is represe

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If the collision frequency of hydrogen molecules in a closed chamber at 27^ C is Z , then the collision frequency of the same system at 127^ C is :

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The translational degrees of freedom (f_t ) and rotational degrees of freedom (f_r ) of CH ₄ molecule are:

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If the root mean square velocity of hydrogen molecule at a given temperature and pressure is 2 km s - 1 , the root mean square velocity of oxygen at the same condition in km s - 1

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Two moles of a monoatomic gas is mixed with six moles of a diatomic gas. The molar specific heat of the mixture at constant volume is :

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A gas mixture consists of 8 moles of argon and 6 moles of oxygen at temperature T . Neglecting all vibrational modes, the total internal energy of the system is

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The parameter that remains the same for molecules of all gases at a given temperature is :

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If three moles of monoatomic gas γ = 5 3 is mixed with two moles of a diatomic gas γ = 7 5 , the value of adiabatic exponent γ for the mixture is:

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At which temperature the r.m.s. velocity of a hydrogen molecule equal to that of an oxygen molecule at 47 ° C ?

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Two thermodynamical process are shown in the figure. The molar heat capacity for process A and B are C A and C B . The molar heat capacity at constant pressure and constant volume

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The temperature of a gas having 2 . 0 × 10 25 molecules per cubic meter at 1 . 38 atm (Given, k = 1 . 38 × 10 - 23 J K - 1 ) is :

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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:

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Two vessels A and B are of the same size and are at same temperature. A contains 1 g of hydrogen and B contains 1 g of oxygen. P A and P B are the pressures of the gases in A and B

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The total kinetic energy of 1 mole of oxygen at 27 ° C is : [Use universal gas constant ( R ) = 8 . 31 J mol - 1 K - 1 ]

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The average kinetic energy of a monatomic molecule is 0 . 414 eV at temperature: (Use K B = 1 . 38 × 10 - 23 J mol - 1 K - 1 )

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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

JEE Main 2023 Solution View → 42

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

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The rms speed of oxygen molecule in a vessel at particular temperature is 1 + 5 x 1 2 v , when v is the average speed of the molecule. The value of x will be: (take π = 22 7 )

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If the r.m.s speed of chlorine molecule is 490 m s - 1 at 27 o C , the r.m.s speed of argon molecules at the same temperature will be (Atomic mass of argon = 39 . 9 u , molecular m

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The root mean square speed of molecules of nitrogen gas at 27 ° C is approximately: (Given mass of a nitrogen molecule = 4 . 6 × 10 - 26 kg and take Boltzmann constant k

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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 con

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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:

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Match List I with List II: List I List II (A) 3 Translational degrees of freedom (I) Monoatomic gases (B) 3 Translational, 2 rotational degrees of freedoms (II) Polyatomic gases (C

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The temperature at which the kinetic energy of oxygen molecules becomes double than its value at 27 ° C is

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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:

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The number of air molecules per cm 3 is increased from 3 × 10 19 to 12 × 10 19 . The ratio of collision frequency of air molecules before and after the increase in number

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The average kinetic energy of a molecule of the gas is

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A flask contains hydrogen and oxygen in the ratio of 2 : 1 by mass at temperature 27 ° C . The ratio of average kinetic energy per molecule of hydrogen and oxygen respectively

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The pressure ( P ) and temperature ( T ) relationship of an ideal gas obeys the equation P T 2 = constant. The volume expansion coefficient of the gas will be :

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At 300 K , the rms speed of oxygen molecules is α + 5 α times to that of its average speed in the gas. Then, the value of α will be (use π = 22 7 )

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The root mean square velocity of molecules of gas is

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Given below are two statements: Statement I : The temperature of a gas is - 73 ° C . When the gas is heated to 527 ° C , the root mean square speed of the molecules is do

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The root mean square speed of smoke particles of mass 5 × 10 - 17 kg in their Brownian motion in air at NTP is approximately. [Given k = 1 . 38 × 10 - 23 J K - 1 ]

JEE Main 2022 Solution View → 59

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 α 2 4 R J mol K - 1 ; then the value of

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A vessel contains 14 g of nitrogen gas at a temperature of 27 ° C . The amount of heat to be transferred to the gas to double the r.m.s. speed of its molecules will be : (Take

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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 molecule

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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 wit

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Same gas is filled in two vessels of the same volume at the same temperature. If the ratio of the number of molecules is 1 : 4 , then A . The r.m.s. velocity of gas molecules in tw

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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

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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 increase

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A vessel contains 16 g of hydrogen and 128 g of oxygen at standard temperature and pressure. The volume of the vessel in cm 3 is :

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What will be the effect on the root mean square velocity of oxygen molecules if the temperature is doubled and oxygen molecule dissociates into atomic oxygen?

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According to kinetic theory of gases, A. The motion of the gas molecules freezes at 0 ° C . B. The mean free path of gas molecules decreases if the density of molecules is inc

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A mixture of hydrogen and oxygen has volume 2000 cm 3 , temperature 300 K , pressure 100 kPa and mass 0 . 76 g . The ratio of number of moles of hydrogen to number of moles of oxyg

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A flask contains argon and oxygen in the ratio of 3 : 2 in mass and the mixture is kept at 27 ° C . The ratio of their average kinetic energy per molecule respectively

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The ratio of specific heats C P C V in terms of degree of freedom f is given by :

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When a gas filled in a closed vessel is heated by raising the temperature by 1 ° C , its pressure increases by 0 . 4 % The initial temperature of the gas is _____ K .

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The relation between root mean square speed v rms and most probable speed v p for the molar mass M of oxygen gas molecule at the temperature of 300 K will be

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A monoatomic gas performs a work of Q 4 where Q is the heat supplied to it. The molar heat capacity of the gas will be _____ R during this transformation. Where R is the gas consta

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0 . 056 kg of Nitrogen is enclosed in a vessel at a temperature of 127 ° C . The amount of heat required to double the speed of its molecules is_____ kcal . (Take R = 2 cal mo

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A uniform heating wire of resistance 36   Ω is connected across a potential difference of 240     V . The wire is then cut into half and a potential difference

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A mixture of hydrogen and oxygen has volume 500 cm 3 , temperature 300 K , pressure 400 k Pa and mass 0 . 76 g . The ratio of masses of oxygen to hydrogen will be:

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For an ideal gas the instantaneous change in pressure P with volume V is given by the equation d P d V = - a P . If P = P 0 at V = 0 is the given boundary condition, then the maxim

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If the R.M.S. speed of oxygen molecules at 0 ° C is 160 m s - 1 . Find the R.M.S. speed of hydrogen molecules at 0 ° C .

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A balloon carries a total load of 185 kg at normal pressure and temperature of 27 ° C . What load will the balloon carry on rising to a height at which the barometric pressure

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A cylindrical container of volume 4 . 0 × 10 - 3 m 3 contains one mole of hydrogen and two moles of carbon dioxide. Assume the temperature of the mixture is 400 K . The pressu

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The R.M.S. speeds of the molecules of Hydrogen, Oxygen, and Carbon dioxide at the same temperature are v H , v O and v C respectively, then:

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The number of molecules in one litre of an ideal gas at 300 K and 2 atmospheric pressure with mean kinetic energy 2 × 10 - 9 J per molecule is:

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Two spherical soap bubbles of radii r 1 and r 2 in vacuum combine under isothermal conditions. The resulting bubble has a radius equal to:

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A system consists of two types of gas molecules A and B having the same number density 2 × 10 25 m - 3 . The diameter of A and B are 10 A and 5 A respectively. They suffer col

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For a gas C P - C V = R in a state P and C P - C V = 1 . 10 R in a state Q , T P and T Q are the temperatures in two different states P and Q , respectively. Then

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What will be the average value of energy for a monoatomic gas in thermal equilibrium at temperature T ?

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The correct relation between the degrees of freedom f and the ratio of specific heat γ is:

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Consider a mixture of gas molecule of types A , B and C having masses m A < m B < m C . The ratio of their root mean square speeds at normal temperature and pressure is:

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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 we

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What will be the average value of energy along one degree of freedom for an ideal gas in thermal equilibrium at a temperature T ? ( k B is Boltzmann constant)

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If one mole of the polyatomic gas is having two vibrational modes and β is the ratio of molar specific heats for polyatomic gas β = C P C v then the value of β is :

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A polyatomic ideal gas has 24 vibrational modes. What is the value of γ ?

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Two ideal polyatomic gases at temperatures T 1 and T 2 are mixed so that there is no loss of energy. If F 1 and F 2 , m 1 and m 2 , n 1 and n 2 be the degrees of freedom, masses, n

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Calculate the value of the mean free path λ for oxygen molecules at temperature 27 ° C and pressure 1 . 01 × 10 5 Pa . Assume the molecular diameter 0 . 3 nm and the

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The volume V of an enclosure contains a mixture of three gases, 16 g of oxygen, 28 g of nitrogen and 44 g of carbon dioxide at absolute temperature T . Consider R as universal gas

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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 mol

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A diatomic gas, having C P = 7 2 R and C V = 5 2 R , is heated at constant pressure. The ratio d U : d Q : d W

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A monoatomic gas of mass 4 . 0   u is kept in an insulated container. The container is moving with velocity 30   m   s - 1 . If the container is suddenly stopped the

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

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The root-mean-square speed of molecules of a given mass of a gas at 27 ° C and 1 atmosphere pressure is 200 m s - 1 . The root-mean-square speed of molecules of the gas at 127

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In a dilute gas at pressure P and temperature ' t ', the time between successive collision of a molecule varies with T as :

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Assuming the nitrogen molecule is moving with r . m . s . velocity at 400 K , the de-Broglie wave length of nitrogen molecule is close to : (Given : nitrogen molecule weight : 4 .6

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Molecules of an ideal gas are known to have three translational degrees of freedom. The gas is maintained at a temperature of T. The total internal energy, U of a mole of this gas,

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Nitrogen gas is at 300 ° C temperature. The temperature (in K ) at which the rms speed of a H 2 molecule would be equal to the rms speed of a nitrogen molecule, is … &#8

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Number of molecules in a volume of 4 cm 3 of a perfect monoatomic gas at some temperature T and at a pressure of 2 cm of mercury is close to? (Given, mean kinetic energy of a molec

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A bullet of mass 5 gram , travelling with a speed of 210 m s - 1 strikes a fixed wooden target. One half of its kinetic energy is converted into heat in the wood. The rise of tempe

JEE Main 2020 Solution View → 108

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

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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 co

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Consider a gas of triatomic molecules. The molecules are assumed to be triangular and made of massless rigid rods whose vertices are occupied by atoms. The internal energy of a mol

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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

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A gas mixture consists of 3 moles of oxygen and 5 moles of argon at temperature T . Assuming the gases to be ideal and the oxygen bond to be rigid, the total internal energy (in un

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Two gases - argon (atomic radius 0.07 n m , atomic weight 40 ) and xenon (atomic radius 0.1 n m , atomic weight 140 ) have the same number density and are at the same temperature.

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Consider two ideal diatomic gases A and B at some temperature T . Molecules of the gas A are rigid, and have a mass m . Molecules of the gas B have an additional vibrational mode a

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Consider a mixture of n moles of helium gas and 2 n moles of oxygen gas (molecules taken to be rigid) as an ideal gas. Its C P C V value will be:

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The plot that depicts the behavior of the mean free time τ (time between two successive collisions) for the molecules of an ideal gas, as a function of temperature T , qualita

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Two moles of an ideal gas, with C P C V = 5 3 , are mixed with three moles of another ideal gas C P C V = 4 3 . The value of C P C V for the mixture is

JEE Main 2020 Solution View → 118

A mixture of two gasses A and B is kept in a vessel which is maintained at a temperature T . In the vessel there are N molecules each of mass m , of the gas A and 2 N molecules eac

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Two identical vessels contain two different ideal gases at the same temperature. If the average speed of gas molecules in the first vessel is equal to the most probable speed of mo

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Two vessels separately contain two ideal gases A and B at the same temperature, the pressure of A being twice that of B . Under such conditions, the density of A is found to be 1.5

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