12Class 11 Physics

Kinetic Theory formulas

The ideal gas and molecular speed formulas for Kinetic Theory. It's a short chapter with very reliable, direct questions.

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All Physics formulas

Ideal gas

Ideal gas law: $\displaystyle pV = nRT = Nk_BT$
Pressure from kinetic theory: $\displaystyle p = \tfrac13\rho\,\overline{v^2}$
Average kinetic energy of a molecule: $\displaystyle \bar K = \tfrac32 k_BT$

Molecular speeds

RMS speed: $\displaystyle v_{\text{rms}} = \sqrt{\frac{3RT}{M}}$
M is the molar mass in kg/mol.
Mean speed: $\displaystyle v_{\text{mean}} = \sqrt{\frac{8RT}{\pi M}}$
Most probable speed: $\displaystyle v_{\text{mp}} = \sqrt{\frac{2RT}{M}}$

Degrees of freedom

Energy per degree of freedom: $\displaystyle E = \tfrac12 k_BT$
Specific heats from f: $\displaystyle C_V = \frac{f}{2}R, \quad C_p = \left(\frac{f}{2} + 1\right)R, \quad \gamma = 1 + \frac{2}{f}$
f = 3 for monatomic and 5 for a rigid diatomic gas.
Mean free path: $\displaystyle \lambda = \frac{1}{\sqrt2\,n\pi d^2}$

Where students slip up

Using molar mass in grams in the speed formulas. It must be in kg/mol.
Using Celsius for T. All of these use kelvin.
Forgetting vᵣₘₛ > vₘₑₐₙ > vₘₚ. The order is a common quick question.

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