Temperature

Temperature is the property of a system that tracks the average kinetic energy of its atoms. It is intensive, so it does not depend on how much of the substance is present, and every gas equation needs it in kelvin.

Temperature enters the AP Physics 2 sheet through one line:

K_{\text{avg}} = \frac{3}{2} k_B T = \frac{1}{2} m v_{\text{rms}}^2

with $k_B = 1.38 \times 10^{-23}$ J/K. Essential knowledge 9.1.B.1 says the same thing in words: the temperature of a system is characterized by the average kinetic energy of the atoms within that system.

Three properties fall out.

It is per atom. $K_{\text{avg}}$ is the average for a single atom. Multiply by the atom count and you have internal energy, which behaves differently.
It is intensive. Halve the sample and the temperature does not move, while the internal energy halves.
Kelvin, with no exceptions. An average kinetic energy cannot be negative, so a scale that runs negative cannot go into these equations. That rules Celsius out of $PV = nRT$ , out of $K_{\text{avg}} = \frac{3}{2}k_B T$ and out of $U = \frac{3}{2}nRT$ .

The one exception is a temperature difference: a change of 25 K and a change of 25 degrees Celsius are the same change, so $Q = mc\Delta T$ tolerates either scale.

Temperature is neither heat nor internal energy. A bathtub and a teacup at 310 K have identical temperatures and wildly different internal energies, and putting them in contact moves no net energy, because temperature alone sets the direction of transfer.

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