Kinetic theory of gases

Also called Kinetic molecular theory, Kinetic theory

Kinetic theory explains the bulk properties of a gas as consequences of the motion and collisions of its atoms. Pressure comes from atoms striking a surface, and temperature tracks their average kinetic energy.

Pressure and temperature are readings you take on a whole gas. Kinetic theory says where each comes from: atoms in motion, colliding with one another and with whatever contains them. AP Physics 2 builds it in Topic 9.1, titled Kinetic Theory of Temperature and Pressure.

Pressure, from collisions. Essential knowledge 9.1.A.1 opens with atoms colliding with and exerting forces on other atoms and on the container. 9.1.A.1.ii then defines the pressure on a surface as the sum of the magnitudes of the perpendicular components of the forces the atoms exert on it, over the area of that surface, which is the sheet's P=F/AP = F_{\perp}/A. Individual collisions are handled with conservation of momentum, per 9.1.A.1.i.

9.1.A.1.iii adds the part that is easy to lose: pressure exists throughout the gas itself, not only at the boundary with the container. A wall is where you can measure it, not where it lives.

Temperature, from average kinetic energy. 9.1.B.1 says the temperature of a system is characterized by the average kinetic energy of the atoms within it, and 9.1.B.1.ii attaches the sheet's

Kavg=32kBT=12mvrms2K_{\text{avg}} = \frac{3}{2}k_BT = \frac{1}{2}mv_{\text{rms}}^2

What the course does not require. The Topic 9.1 boundary statement says students are not expected to know the functional form of the Maxwell-Boltzmann distribution, only how its features relate to the temperature of the gas. So heating a gas shifts that curve toward higher speeds, and the exam asks you to describe it rather than compute it.

The speed itself is root-mean-square speed; the equation of state the model produces is the ideal gas law.

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