A sample of monoatomic gas Y has a volume of 800 mm³, P = 3.0 atm, and T = 150℃. A different sample contains neon at V = 1750 mm³, P = 5.0 atm, and T = 250℃. The two samples are allowed to interact thermally through a boundary. Calculate the thermal energy of each sample when thermal equilibrium is attained. 

A hypothetical gas with 4 atoms bonded in a T-shape has a high bond energy that requires temperatures greater or equal to 1200K to activate vibrational modes. The hypothetical gas has rotational kinetic energy in a 3D coordinate system at all temperatures. Calculate the thermal energy of a sample of the gas with n = 6.2 mol, at T = 350 °C. 

Constant pressure of a gas sample can be attained by fitting a container with a movable piston. A gas in such a container is maintained at a constant pressure of 800 Pa. If the gas is oxygen (molar mass 32.00 g/mol) and its temperature varies between 40°C and -70°C, calculate the range of root-mean-square speeds for oxygen molecules.

A gas molecule is at a temperature of 15°C and is moving at a random rms speed. Find the ratio of new rms speed to old rms speed if the temperature of the molecule is raised to 2000°C.

Assuming that pollen grains are spherical and have a density of 1100 kg/m³, calculate the rms speed of a pollen grain at a temperature of 25°C if it behaves like an ideal gas. The diameter of a typical pollen grain is 20 μm.

Determine the mean free path of a molecule in a gas if the gas temperature is increased by a factor of 4, given the gas is kept at i) constant volume, and ii) constant pressure. Initially, the molecule has a mean free path of 450 nm.

At a given temperature and pressure, the mean free path of a helium atom in a gas sample is 300 nm. If the gas sample is replaced with an argon gas sample at the same temperature and pressure, what is the mean free path of an argon atom?

The atmosphere of a terrestrial exoplanet is composed primarily of nitrogen. The temperature and pressure at the surface of the exoplanet are thought to be 430 K and 15 bars, respectively. The planetary scientists studying this exoplanet define the standard temperature and pressure (STP) as 430 K and 15 bars, respectively. Calculate i) the mean free path and ii) the root mean square velocity of nitrogen molecules on the planet's surface. Assume that the ideal gas law is applicable. The two nitrogen atoms are separated by a distance of 1.3 × 10⁻¹⁰ m.

Oxygen is a diatomic gas with a molar mass of 32.00 g/mol. Determine its average speed (v_av) at 273 K.