Kinetic Theory of Gases

A fixed amount of gas occupies 4 L at 1 atm and 300 K. Find its volume at 2 atm and 450 K.

Find the rms speed of oxygen molecules at 300 K. (Molar mass of O₂ = 32 × 10⁻³ kg/mol, R = 8.3 J/mol·K)

If the absolute temperature of a gas is increased 4 times, by what factor does the rms speed of its molecules increase?

Find the average translational kinetic energy of a gas molecule at 400 K. (Boltzmann constant k = 1.38 × 10⁻²³ J/K)

Find the total translational kinetic energy of 1 mole of an ideal gas at 500 K. (R = 8.3 J/mol·K)

For a gas at any given temperature, how do the rms speed (v_rms), average speed (v_avg), and most probable speed (v_p) of its molecules compare?

A diatomic gas has 7 degrees of freedom per molecule (translational + rotational + vibrational, at high temperature). Find its ratio of specific heats, γ.

If the number density of molecules in a gas is doubled while temperature and molecular size stay the same, how does the mean free path change?

Find the mean free path of molecules in a gas with number density 2 × 10²⁵ m⁻³ and effective molecular diameter 2 × 10⁻¹⁰ m.

In the Van der Waals equation (P + a/V²)(V−b) = RT, what does the constant 'a' physically account for?

Calculate the Boltzmann constant, given R = 8.3 J/mol·K and Avogadro's number N_A = 6.02 × 10²³/mol.

A gas has density 1.2 kg/m³ and an rms molecular speed of 500 m/s. Find its pressure.

An ideal gas of volume 0.02 m³ has a total translational kinetic energy of 300 J. Find its pressure.

Find the ratio of the rms speed of hydrogen molecules (M = 2 g/mol) to that of oxygen molecules (M = 32 g/mol) at the same temperature.

Two different ideal gases, of different molar masses, are kept at the same temperature. How do their average translational kinetic energies per molecule compare?

Find the molar specific heat at constant volume (C_v) for a diatomic gas with 5 degrees of freedom. (R = 8.3 J/mol·K)

Find the number of molecules present in 2 moles of an ideal gas. (N_A = 6.02 × 10²³ /mol)

Find the most probable speed of nitrogen molecules at 300 K. (Molar mass of N₂ = 28 × 10⁻³ kg/mol, R = 8.3 J/mol·K)