Average Kinetic Energy of Gases Practice Problems

What is the mean translational kinetic energy of atmospheric nitrogen (N2) of molar mass 28.01 g/mol at a temperature of 298 K?

In a physics simulation, four particles are moving with unique velocities as follows:
v₁ = (10î - 20ĵ) m/s
v₂ = (30î + 40ĵ) m/s
v₃ = (-40î + 10ĵ) m/s
v₄ = (20î - 30ĵ) m/s

Determine i) Average velocity (v_avg), ii) Average speed (v_avg), and iii) Root-mean-square velocity (v_rms) of the particles in the simulation.

A container holds 1.5 moles of neon gas, which possesses 2500 J of thermal energy. Calculate the temperature of the gas in degrees Celsius.

In a container at atmospheric pressure, the temperature of the krypton gas above the liquid krypton is at krypton's boiling point of 120 K. Determine (i) the root-mean-square speed of the atoms, (ii) the mean energy per atom, and (iii) the mean free path in the gas. The atomic mass of krypton is 83.798 u and the atomic radius of krypton is 8.8 x 10^-11 m.

In an experiment, a 3.0 g sample of argon gas was enclosed in a special chamber. If the rms speed of the atoms inside the chamber is 900 m/s, determine the total thermal energy of the argon gas.

In an art gallery, a cubic room with sides measuring 10 m each maintains a consistent air temperature of 24℃ to preserve the artwork. Calculate the total thermal energy of the room.

In a helium ion He⁺, the energy required to excite an electron from the ground state (𝑛 = 1) to the first excited state (𝑛 = 2) is 40.8 eV. Determine the temperature at which the average kinetic energy of a helium ion is sufficient to excite an electron from the 𝑛 = 1 state to the 𝑛 = 2 state. Use Boltzmann constant k = 8.617 × 10⁻⁵ eV/K.

When a cesium atom has an electron that transitions from an excited state to the ground state, it releases a photon with a wavelength of 850 nm. Determine the resulting nonrelativistic recoil speed 𝑣 of the atom. (Hint: The mass of a cesium atom is 133 u.)

The recoil speed sets the lower limit on the temperature to which an atom of an ideal gas can be cooled in a laser-based atom trap. When an initially excited electron of a cesium atom (mass = 133 u) jumps to the ground state, the atom emits a photon with a wavelength 𝜆=850 nm. The resulting nonrelativistic recoil speed 𝑣 of the cesium atom is 3.53×10⁻³ m/s. Using the kinetic theory of gases, estimate this “lowest achievable” temperature.