Kinetic Theory formulas
Class 11 physics formula sheet for NEET and JEE: the key equations of NCERT chapter 12, the special cases questions are built on, and diagrams where they help.
By Sreeraj P, M.Sc Physics · 10+ years teaching NEET and JEE
Most used formulasOther formulas and cases
1Gas laws and ideal gas
$$PV=nRT=Nk_BT,\qquad P=\frac{\rho RT}M,\qquad \frac{P_1V_1}{T_1}=\frac{P_2V_2}{T_2}$$
$$\begin{array}{l}\displaystyle PV=nRT=Nk_BT\\[6pt]\displaystyle P=\frac{\rho RT}M\\[6pt]\displaystyle \frac{P_1V_1}{T_1}=\frac{P_2V_2}{T_2}\end{array}$$
$R=8.314$ J mol⁻¹ K⁻¹, $k_B=1.38\times10^{-23}$ J K⁻¹, $N_A=6.02\times10^{23}$. 1 mol at STP: 22.4 L. Boyle ($T$ const): $PV$ const, $P\propto\rho$. Charles ($P$ const): $V\propto T$, $V_t=V_0(1+t/273)$. Gay-Lussac ($V$ const): $P\propto T$. Avogadro: equal volumes, same $P,T$ → equal molecules.
| Case | Result |
|---|---|
| Quill tube, mercury pellet $h$ (length of air $l$) | $Pl$ const: open end up $(P_0+h)l_1$, down $(P_0-h)l_2$, horizontal $P_0l_3$; at angle $\theta$: $P_0\pm h\sin\theta$ |
| Air bubble rising from depth $h$ (constant $T$) | $V_{\text{top}}=V\dfrac{P_0+\rho gh}{P_0}$; radius ratio cube root |
| Tube inverted in mercury, air trapped | $(P_0-h)\times(\text{air length})$ = const |
| Two vessels joined by a tube (same $T$) | $P=\dfrac{P_1V_1+P_2V_2}{V_1+V_2}$ (Dalton mixing) |
| Vessels at different $T$ joined | moles conserved: $\dfrac{P_1V_1}{T_1}+\dfrac{P_2V_2}{T_2}=P\left(\dfrac{V_1}{T_1'}+\dfrac{V_2}{T_2'}\right)$ |
| Gas leaks out of a vessel heated at constant $P$ | fraction left $=\dfrac{T_1}{T_2}$ |
| Pump strokes (vessel $V$, barrel $v$) | exhaust: $P_n=P_0\left(\dfrac V{V+v}\right)^n$; compression: $P_n=P_0\left(1+\dfrac{nv}V\right)$ |
| Graphs | $P$–$V$ at const $T$: hyperbola; $PV$–$P$: horizontal line; $V$–$T$ at const $P$: line through origin, slope $\propto1/P$ |
- Dalton: $P=P_1+P_2+\dots$ Real gases follow ideal behaviour at low pressure and high temperature. Van der Waals: $\left(P+\dfrac{an^2}{V^2}\right)(V-nb)=nRT$.
3 more sections and 12 formulas in the full chapter
- 2Kinetic theory: pressure and speeds7 formulas · 1 diagram
- 3Equipartition and specific heats4 formulas · 1 case table
- 4Mean free path1 formula
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