What is the total translational kinetic energy of 1.0 mol of N₂ molecules at 25°C?

Consider a container like that shown in Figure, with $n_1$ moles of a monatomic gas on one side and $n_2$ moles of a diatomic gas on the other. The monatomic gas has initial temperature $T_{1i}$. The diatomic gas has initial temperature $T_{2i}$. Show that the equilibrium thermal energies are

$\begin{aligned}E_{1f} &= \frac{3n_1}{3n_1 + 5n_2} (E_{1i} + E_{2i}) \\E_{2f} &= \frac{5n_2}{3n_1 + 5n_2} (E_{1i} + E_{2i})\end{aligned}$

Estimate the time needed for a glycine molecule (see Table 18–3) to diffuse a distance of 25μm in water at 20°C if its concentration varies over that distance from 1.00 mol/m³ to 0.50 mol/m³. Compare this “speed” to its rms (thermal) speed. The molecular mass of glycine is about 75 u.

At about what pressure would the mean free path of air molecules be equal to the diameter of air molecules, ≈ 3 x 10⁻¹⁰ m? Assume T = 20° C.

(I) What speed would a 1.5-g paper clip have if it had the same kinetic energy as a molecule at 22°C?

A 1.0-mol sample of helium gas has a temperature of 18°C. What is the total kinetic energy of all the gas atoms in the sample?

(I) Approximately how long would it take for the ammonia of Example 18–9 to be detected 1.0 m from the bottle after it is opened? What does this suggest about the relative importance of diffusion and convection for carrying odors?

A 1.0-mol sample of helium gas has a temperature of 18°C. How fast would a 65-kg person have to run to have the same kinetic energy?

A 0.40-kg trash-can lid is suspended against gravity by tennis balls thrown vertically upward at it. How many tennis balls per second must rebound from the lid elastically, assuming they have a mass of 0.060 kg and are thrown at 15 m/s?