Kinetic Theory of Gases

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 mixture respectively are ______. (Assume both carbon dioxide and oxygen gases behave like ideal gases) [R = 8.31 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 $\mathrm{H_2}$ 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

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.

For a diatomic gas, if $\gamma_1 = \left(\dfrac{C_p}{C_v}\right)$ for rigid molecules and $\gamma_2 = \left(\dfrac{C_p}{C_v}\right)$ 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)

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 :

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

A container of fixed volume contains a gas at $27^\circ$C. To double the pressure of the gas, the temperature of gas should be raised to ______ $^\circ$C.

$\gamma_A$ 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 $\frac{\gamma_A}{\gamma_B} = \left(1 + \frac{1}{n}\right)$, then the value of n is ______.