Chapter 21: The Kinetic Theory of Gases

Root mean square (rms) speed

At a given temperature, lighter molecules move faster while heavier molecules move slower

Theorem of equipartition of energy

In general, a "degree of freedom" refers to an independent means by which a molecule can possess energy. Each dimension a molecule can move is a degree of freedom

What is the average kinetic energy per molecule of a gas?

It's half its mass and average speed squared

What is the total translational kinetic energy of N molecules?

Its N times the average kinetic energy per molecule of a gas. If the gas molecules possess only translational kinetic energy then this is also the internal energy of the gas

What is the internal energy of N molecules (or n moles) of gas at a temperature T (assume a monatomic ideal gas)?

N=number of atoms kb=Boltzman's constant (1.381 e-23 m² kg s⁻² K⁻¹)

Relate the pressure of a gas to it's number of molecules per unit volume and it's molecular kinetic energy

The pressure of a gas is proportional to it's numbers of molecules per unit volume and it's average translational kinetic energy of all it's molecules

Relate the temperature of a gas to it's average molecular kinetic energy

The temperature of a gas is proportional to to the average molecular kinetic energy

What are process variables? Give examples

Variables that depend on the path that we take through state space. They include work (W) and heat (Q)

What are state variables? Give examples

Variables that only depend on the current state of the system. Examples include, pressure (P), volume (V), temperature (T), mole number (n), particle number (N), internal energy (Eint. or U), and entropy (S)