Thermodynamics formulas
Class 11 physics formula sheet for NEET and JEE: the key equations of NCERT chapter 11, 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
1Zeroth and first law
- Zeroth law: A and B each in thermal equilibrium with C are in equilibrium with each other → temperature.
- State variables ($P,V,T,U$) depend only on the state; $Q$ and $W$ depend on the path. Intensive: $P,T,\rho$; extensive: $V,U,m$.
$$\begin{array}{l}\displaystyle Q=\Delta U+W,\quad W=\int P\,dV\\[5pt]\displaystyle \Delta U=nC_V\Delta T\ (\text{any process, ideal gas})\end{array}$$
$Q>0$ absorbed, $W>0$ done by the gas (expansion). $W$ = area under the $P$–$V$ curve. Same end states by two paths: $\Delta U$ same, so $Q_1-W_1=Q_2-W_2$. Cycle: $\Delta U=0$, $Q_{\text{net}}=W_{\text{net}}=$ enclosed area (clockwise on $P$–$V$: positive).
| Case | Result |
|---|---|
| Water → steam at 100 °C, 1 atm | $W=P(V_s-V_w)$, $\Delta U=mL-W$ |
| Gas container moving at $v$ stopped suddenly | $\tfrac12Mv^2\,(\text{per mole})=C_V\Delta T\Rightarrow\Delta T=\dfrac{Mv^2(\gamma-1)}{2R}$ |
| Free expansion into vacuum (insulated) | $Q=0$, $W=0$, $\Delta U=0$, $T$ constant (ideal gas); irreversible |
| Block sliding on ice, friction | ice melted $=\dfrac{\mu mgd}{L}$ |
| $U$ given as $a+bPV$ | $C_V=bR$, $\gamma=1+\dfrac1b$ |
3 more sections and 14 formulas in the full chapter
- 2Specific heats of gases6 formulas
- 3Thermodynamic processes3 formulas · 2 case tables · 1 diagram
- 4Second law, engines and refrigerators5 formulas · 1 case table
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