Thermal Properties of Matter formulas

Class 11 physics formula sheet for NEET and JEE: the key equations of NCERT chapter 10, the special cases questions are built on, and diagrams where they help.

33 formulas6 sectionsClass 11 · Chapter 102 of 6 sections free

By Sreeraj P, M.Sc Physics · 10+ years teaching NEET and JEE

Most used formulasOther formulas and cases

1Temperature and thermometry

$$\begin{array}{l}\displaystyle \frac{C}{100}=\frac{F-32}{180}=\frac{K-273.15}{100}=\frac R{80}\\[5pt]\displaystyle \frac{X-\text{LFP}}{\text{UFP}-\text{LFP}}=\text{same on every scale}\end{array}$$

Differences: $\Delta C:\Delta F:\Delta K=5:9:5$. $-40^\circ$C $=-40^\circ$F; $574.6$ K $=574.6^\circ$F. Slope of $F$ vs $C$ graph $=9/5$.

$$t=\frac{X_t-X_0}{X_{100}-X_0}\times100^\circ\text{C},\qquad T=273.16\,\frac{X}{X_{tr}}\ \text{K}$$

$$\begin{array}{l}\displaystyle t=\frac{X_t-X_0}{X_{100}-X_0}\times100^\circ\text{C}\\[6pt]\displaystyle T=273.16\,\frac{X}{X_{tr}}\ \text{K}\end{array}$$

Any property varying linearly ($P$ at constant $V$, $V$ at constant $P$, resistance). Triple point of water 273.16 K (0.01 °C). Platinum: $R_t=R_0(1+\alpha t)$.

2Thermal expansion of solids

$$\begin{array}{l}\displaystyle l=l_0(1+\alpha\Delta\theta),\quad A=A_0(1+\beta\Delta\theta),\quad V=V_0(1+\gamma\Delta\theta)\\[5pt]\displaystyle \alpha:\beta:\gamma=1:2:3\end{array}$$

$$\begin{array}{l}\displaystyle l=l_0(1+\alpha\Delta\theta)\\[6pt]\displaystyle A=A_0(1+\beta\Delta\theta)\\[6pt]\displaystyle V=V_0(1+\gamma\Delta\theta)\\[6pt]\displaystyle \alpha:\beta:\gamma=1:2:3\end{array}$$

Anisotropic: $\gamma=\alpha_x+\alpha_y+\alpha_z$. On the Fahrenheit scale $\alpha_F=\tfrac59\alpha_C$. Holes and cavities expand as if filled with the material; solid and hollow spheres of the same outer radius expand equally.

$$\rho=\rho_0(1-\gamma\Delta\theta),\qquad \frac{\Delta I}I=2\alpha\Delta\theta,\qquad \omega'=\omega(1-2\alpha\Delta\theta)$$

$$\begin{array}{l}\displaystyle \rho=\rho_0(1-\gamma\Delta\theta)\\[6pt]\displaystyle \frac{\Delta I}I=2\alpha\Delta\theta\\[6pt]\displaystyle \omega'=\omega(1-2\alpha\Delta\theta)\end{array}$$

Density falls on heating; a spinning body slows on heating ($L$ conserved).

Case	Result
Composite rod $l_1,l_2$	$\Delta l=(l_1\alpha_1+l_2\alpha_2)\Delta\theta$, $\alpha_{\text{eff}}=\dfrac{l_1\alpha_1+l_2\alpha_2}{l_1+l_2}$
Difference of lengths constant at all $\theta$	$l_1\alpha_1=l_2\alpha_2$; $l_1=\dfrac{x\alpha_2}{\alpha_1-\alpha_2}$, $l_2=\dfrac{x\alpha_1}{\alpha_1-\alpha_2}$
Metal scale reading at $\theta$ (calibrated at $\theta_0$)	true $=$ reading $\times[1+\alpha_s(\theta-\theta_0)]$; reads less when hot. Scale and body: $l_c=l_m[1+(\alpha_s-\alpha_b)\Delta\theta]$
Pendulum clock	$\dfrac{\Delta T}T=\tfrac12\alpha\Delta\theta$; loses $\tfrac12\alpha\Delta\theta\times86400$ s/day when hotter. Compensated: $l_1\alpha_1=l_2\alpha_2$
Bimetallic strip (each thickness $d$)	$R=\dfrac{d}{(\alpha_2-\alpha_1)\Delta\theta}$; higher $\alpha$ on the convex side when heated
Rail of length $L$ buckles (fixed ends)	centre rises $\approx\dfrac L2\sqrt{2\alpha\Delta\theta}$
Barometer with brass scale	$h_0=h_t[1-(\gamma_{Hg}-\alpha_s)t]$
Balance wheel / torsion clock	gains or loses $\alpha\Delta\theta\times86400$ s/day

$$\text{stress}=Y\alpha\Delta\theta,\qquad F=YA\alpha\Delta\theta,\qquad P=B\gamma\Delta\theta$$

$$\begin{array}{l}\displaystyle \text{stress}=Y\alpha\Delta\theta\\[6pt]\displaystyle F=YA\alpha\Delta\theta\\[6pt]\displaystyle P=B\gamma\Delta\theta\end{array}$$

Rod between rigid walls: force independent of length. Two rods in series between walls: $F=\dfrac{(l_1\alpha_1+l_2\alpha_2)\Delta\theta}{l_1/Y_1A+l_2/Y_2A}$; junction does not shift if $\alpha_1Y_1=\alpha_2Y_2$ (equal lengths). Ring shrunk on a wheel: $T=SY\alpha\Delta\theta$, force between halves $2SY\alpha\Delta\theta$. Wire cooled to support a load: $mg=YA\alpha\Delta\theta$.

4 more sections and 19 formulas in the full chapter

3Expansion of liquids and gases3 formulas · 1 case table
4Calorimetry and change of state4 formulas · 1 case table · 1 diagram
5Conduction3 formulas · 1 case table
6Radiation9 formulas

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