The RMS speed of 65 g of oxygen gas is 254 m/s. Calculate the average kinetic energy of the molecules.

The molecules in a six-particle gas have velocities:

$\begin{aligned}\vec{v}_1 &= (20\hat{i} - 30\hat{j}) \text{ m/s} \\\vec{v}_2 &= (40\hat{i} + 70\hat{j}) \text{ m/s} \\\vec{v}_3 &= (-80\hat{i} + 20\hat{j}) \text{ m/s} \\\vec{v}_4 &= 30\hat{i} \text{ m/s} \\\vec{v}_5 &= (40\hat{i} - 40\hat{j}) \text{ m/s} \\\vec{v}_6 &= (-50\hat{i} - 20\hat{j}) \text{ m/s}\end{aligned}$

Calculate (a) ${\vec{v}}_{\text{avg}}$, (b) $v_{\text{avg}}$, and (c) $v_{\text{rms}}$.

At what temperature would the average kinetic energy (Chapter 18) of a molecule of hydrogen gas (H₂) be sufficient to excite a hydrogen atom out of the ground state?

A rubidium atom (m = 85 u) is at rest with one electron in an excited energy level. When the electron jumps to the ground state, the atom emits a photon of wavelength ⋋ = 780 nm. Determine the resulting (nonrelativistic) recoil speed v of the atom.

A rubidium atom (m = 85 u) is at rest with one electron in an excited energy level. When the electron jumps to the ground state, the atom emits a photon of wavelength ⋋ = 780 nm. The recoil speed sets the lower limit on the temperature to which an ideal gas of rubidium atoms can be cooled in a laser-based atom trap. Using the kinetic theory of gases (Chapter 18), estimate this “lowest achievable” temperature.

In a sample of gas, you pick a particle at random. The mass of the particle is 1.67 × 10^-27 kg and you measure its speed to be 1600 m/s. If that particle's kinetic energy is equal to the average kinetic energy of the gas particles, what is the temperature of the sample of gas?

Oxygen (O₂) has a molar mass of $32.0$ g/mol. What is the average translational kinetic energy of an oxygen molecule at a temperature of $300$ K?

A 6.0 m ✕ 8.0 m ✕ 3.0 m room contains air at 20℃. What is the room's thermal energy?

The rms speed of the atoms in a 2.0 g sample of helium gas is 700 m/s. What is the thermal energy of the gas?