Kinetic Theory of Gases — JEE Main PYQs

A mixture of carbon dioxide and oxygen has volume $8310 \text{ cm}^3$, temperature 300 K, pressure 100 kPa and mass 13.2 g. The number of moles of carbon dioxide and oxygen gases in the mixture respectively are ________.

(Assume both carbon dioxide and oxygen gases behave like ideal gases) [$R = 8.31 \text{ J/mol.K}$]

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 __________.

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 $\text{H}_2$ and $\text{O}_2$ molecules, kept in two different sized containers are same, then their temperatures will be same.

Reason R: The r.m.s. speed of $\text{H}_2$ and $\text{O}_2$ molecules are same at same temperature.

Choose the correct answer from the options given below

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 gas can be written as $\Delta U = n\,C_V\left(T_{\text{f}} - T_i\right) = \dfrac{nR}{\gamma - 1}\left(T_{\text{f}} - T_i\right)$, where $\gamma = \dfrac{C_p}{C_v}$, $T_i$ = initial temperature, $T_{\text{f}}$ = final temperature.

Statement II: Relation between degree of freedom $f$ and $\gamma$ ($= C_p/C_v$) is $\left(\gamma = 1 + \dfrac{2}{f}\right)$

Choose the correct answer from the options given below

Two closed vessels of same volume are joined through a narrow tube and both vessels are filled with air of pressure 90 kPa and temperature 400 K. Keeping the temperature of one vessel constant at 400 K the second vessel temperature is raised to 500 K. The final pressure in the vessels is ________ kPa.

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 :

$\gamma_A$ is the specific heat ratio of monoatomic gas A having 3 translational degrees of freedom. $\gamma_B$ is the specific heat ratio of polyatomic gas B having 3 translational, 3 rotational degrees of freedom and 1 vibrational mode. If $\dfrac{\gamma_A}{\gamma_B}=\left(1+\dfrac{1}{n}\right)$, then the value of n is _________.

The internal energy of air in $4~\mathrm{m}\times4~\mathrm{m}\times3~\mathrm{m}$ sized room at 1 atmospheric pressure will be _________ $\times10^{6}$ J.

(Consider air as diatomic molecule)

Pressure of an ideal gas, contained in a closed vessel, is increased by 0.4% when heated by 1°C. Its initial temperature must be:

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).

Match the LIST-I with LIST-I

LIST-I	LIST-II
A. Triatomic rigid gas	I. $\frac{C_p}{C_v} = \frac{5}{3}$
B. Diatomic non-rigid gas	II. $\frac{C_p}{C_v} = \frac{7}{5}$
C. Monoatomic gas	III. $\frac{C_p}{C_v} = \frac{4}{3}$
D. Diatomic rigid gas	IV. $\frac{C_p}{C_v} = \frac{9}{7}$

Choose the correct answer from the options given below:

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 helium $= 4$ g/mol, Molar mass of argon $= 40$ g/mol)

For a diatomic gas, if $\gamma_1 = \left(\frac{C_p}{C_v}\right)$ for rigid molecules and $\gamma_2 = \left(\frac{C_p}{C_v}\right)$ for another diatomic molecules, but also having vibrational modes. Then, which one of the following options is correct ?

($C_p$ and $C_v$ are specific heats of the gas at constant pressure and volume)

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

The kinetic energy of translation of the molecules in 50 g of $\mathrm{CO_2}$ gas at 17°C is

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

P-T diagram of an ideal gas having three different densities $\rho_1$, $\rho_2$, $\rho_3$ (in three different cases) is shown in the figure. Which of the following is correct :

[Figure: P vs T graph with three straight lines from the origin, with slopes decreasing in the order $\rho_1$, $\rho_2$, $\rho_3$ (line $\rho_1$ steepest)]

The translational degrees of freedom ($f_t$) and rotational degrees of freedom ($f_r$) of $CH_4$ molecule are:

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 :

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 represented by :

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

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

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 respectively is:

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 energy of gas molecules is directly proportional to absolute temperature of gas.

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

The temperature of a gas is $-78°\mathrm{C}$ and the average translational kinetic energy of its molecules is K. The temperature at which the average translational kinetic energy of the molecules of the same gas becomes 2K is :

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

The average kinetic energy of a monoatomic molecule is 0.414 eV at temperature :

(Use $\mathrm{K_B} = 1.38 \times 10^{-23}$ J/mol-K)

Two vessels A and B are of the same size and are at same temperature. A contains 1g of hydrogen and B contains 1g of oxygen. $\mathrm{P_A}$ and $\mathrm{P_B}$ are the pressures of the gases in A and B respectively, then $\frac{P_A}{P_B}$ is :

At which temperature the r.m.s. velocity of a hydrogen molecule equal to that of an oxygen molecule at $47~°\mathrm{C}$ ?

If three moles of monoatomic gas $\left(\gamma = \frac{5}{3}\right)$ is mixed with two moles of a diatomic gas $\left(\gamma = \frac{7}{5}\right)$, the value of adiabatic exponent $\gamma$ for the mixture is

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

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: