Ideal Gases Kinetic Theory of Gases Thermal Physics Ideal Gases Kinetic Theory of Gases

Ideal Gases – Variables P is the ________ V is the ________ T is the ___________ (K) n is the ________ of gas (moles) For low P (low densities) the gas is called _____ Avogadro’s Number, NA, is the number of _________ per mole Chosen so that the mass of NA particles is equal to _______ mass

n and Equation of State Molar mass is the mass of ______ _______ of substance (use periodic table, e.g. SiO2→60 g/mol) N is the number of molecules Equation of State Universal Gas Constant Boltzmann’s Constant

Kinetic Theory – Assumptions Large number of molecules – average separation _____ compared to their size. Molecules obey Newton’s Laws , but motion is ______. Molecules interact ___________ via short-range forces. Molecules make _______ collisions with the walls of the container. All molecules in a gas are _________.

Quantities Describing Gases _____ Variables describe the macroscopic state of the gas: Pressure P Volume V Temperature T ___________ Variables describe the individual molecules or atoms: Mass m Velocity v

Connecting Macroscopic to Microscopic – Pressure d Use ______-Momentum Let Δt to be time for a round trip (1 collision with left wall for each round trip) Fig. 10.14, p. 341

Connecting Macroscopic to Microscopic – Pressure (cont’d) Add contributions from all N molecules Average value of squared velocity is Total force is

Connecting Macroscopic to Microscopic – Pressure (cont’d) Speed and the Pythagorean Theorem Since motion in each direction is completely ______ Giving

Connecting Macroscopic to Microscopic – Pressure (cont’d) Total force is Divide by area A = d 2 to find the pressure

Ideal Gas Law – Revisited Average translational kinetic energy per molecule For monatomic gas

Root-Mean-Square Velocity Connects macroscopic to microscopic M is _____ mass in kg/mol