Atomic/molecular collisions and pressure The kinetic-molecular theory relates pressure to elastic collisions between individual particles and the walls of the container. Even though atoms/molecules are light, they move at hundreds or even thousands of m/s, and each contributes significant kinetic energy.

Q18.3 Consider two specimens of ideal gas at the same temperature. The molecules in specimen #1 have greater molar mass than the molecules in specimen #2. How do the rms speed of molecules (vrms) and the average translational kinetic energy per molecule (KE) compare in the two specimens? A. vrms and KE are both greater in specimen #2. B. vrms is greater in specimen #2; KE is the same in both specimens. C. vrms is greater in specimen #2; KE is greater in specimen #1. D. Both vrms and KE are the same in both specimens. E. None of the above is correct.

A18.3 Consider two specimens of ideal gas at the same temperature. The molecules in specimen #1 have greater molar mass than the molecules in specimen #2. How do the rms speed of molecules (vrms) and the average translational kinetic energy per molecule (KE) compare in the two specimens? A. vrms and KE are both greater in specimen #2. B. vrms is greater in specimen #2; KE is the same in both specimens. C. vrms is greater in specimen #2; KE is greater in specimen #1. D. Both vrms and KE are the same in both specimens. E. None of the above is correct.

Speed of air molecules What is the average translational kinetic energy of one molecule of an ideal gas of oxygen (molar mass M = 32 g/mol) at 27°C? What about nitrogen (molar mass M = 28 g/mol)? What is the rms speed of nitrogen and oxygen?

Expanding Helium Helium gas starts at a volume Vi = 1L = 0.001m3 and Pi = 1 atm. It expands linearly (on pV diagram) to Vf = 3L = 0.003m3 and Pf = 3 atm. Draw the pV diagram for this process What is the work done by the gas when it expands? What is its increase in thermal energy? How much heat is gained or lost by the gas?

Illustration of heat absorption into degrees of freedom

How much heat energy can ensembles contain? An atom can absorb energy as the kinetic energy of its motion. A molecule can absorb energy in its translation, and also in its rotation and in the vibrations of one atom in its structure with respect to the others. Atomic/molecular energy absorbed is termed its “heat capacity.”

Energy of monatomic and diatomic gases How much heat is required to raise 4g of He gas from 300 K to 310 K at constant volume? How about hydrogen gas H2? What is the rms speed of He gas and H2 at 300K?

Measuring atomic/molecular speeds Beams of molecules are created in a vacuum chamber where the pressure is low enough to have a mean free path at least 10 × farther than the sample path. (A typical apparatus would require 10−6 torr to obtain mean free path ~10–100 m and accommodate a 1 m experimental setup.)

Molecules form distributions of velocities A temperature-dependent distribution forms around the most likely velocity for a given sample.