Thermal Physics

Thermal physics studies the behaviour of matter through the relationship between heat, work, temperature, and energy. It bridges the microscopic world of molecular motion with the macroscopic properties of gases, solids, and liquids.

Topics Covered

Thermal Properties

• Temperature scales — Celsius, Kelvin; $T(\text{K}) = T(^{\circ}\text{C}) + 273.15$; absolute zero as the theoretical minimum
• Specific heat capacity — $Q = mc\Delta T$; energy required to raise the temperature of 1 kg by 1 K; continuous flow method for measurement
• Specific latent heat — $Q = mL$; energy for change of state at constant temperature; fusion (solid $\to$ liquid) and vaporisation (liquid $\to$ gas)
• Internal energy — the sum of kinetic and potential energy of all molecules; increased by heating or doing work

Ideal Gas Laws

• Boyle’s law — $pV = \text{constant}$ at constant $T$; inverse proportionality of pressure and volume
• Charles’s law — $V/T = \text{constant}$ at constant $p$; volume proportional to temperature (Kelvin)
• Pressure law — $p/T = \text{constant}$ at constant $V$
• Ideal gas equation — $pV = nRT$ (molar form) and $pV = NkT$ (molecular form); $R = 8.31\,\text{J mol}^{-1}\text{K}^{-1}$, $k = 1.38 \times 10^{-23}\,\text{JK}^{-1}$

Kinetic Theory

• Assumptions — point particles, elastic collisions, random motion, large number of particles, negligible intermolecular forces (except during collisions)
• Root mean square speed — $c_{\text{rms}} = \sqrt{\frac{c_1^2 + c_2^2 + \cdots + c_N^2}{N}}$
• Pressure derivation — $pV = \frac{1}{3}Nm c_{\text{rms}}^2$; connecting microscopic motion to macroscopic pressure
• Kinetic energy and temperature — $\frac{1}{2}m c_{\text{rms}}^2 = \frac{3}{2}kT$; temperature is a measure of average kinetic energy per molecule
• Maxwell-Boltzmann distribution — the distribution of molecular speeds; effect of temperature on the shape of the distribution

Thermodynamics

• First law — $\Delta U = Q - W$; change in internal energy = heat supplied minus work done by the gas
• Work done by a gas — $W = p\Delta V$ (at constant pressure); area under a $p$-$V$ graph
• Isothermal and adiabatic processes — isothermal ($\Delta T = 0$, heat exchanged); adiabatic ($Q = 0$, no heat exchange, temperature changes)

Study Tips

1. Derive the kinetic theory equation — $pV = \frac{1}{3}Nm c_{\text{rms}}^2$ — from first principles (momentum change at a wall). This derivation is frequently examined.
2. Sketch Maxwell-Boltzmann curves — be able to draw the distribution for two different temperatures and explain how the peak shifts and broadens.
3. Know the gas law experiments — how to verify Boyle’s law (pressure pump and volume measurement), Charles’s law (capillary tube in water bath).
4. Connect $pV = nRT$ and $pV = \frac{1}{3}Nm c_{\text{rms}}^2$ — equating them gives $\frac{1}{2}m c_{\text{rms}}^2 = \frac{3}{2}kT$, linking kinetic energy to temperature.
5. Practise first law calculations — identify whether $Q$, $W$, and $\Delta U$ are positive, negative, or zero for different processes (isothermal expansion, adiabatic compression, etc.).

How to Use These Notes

Follow the sidebar order. Each page provides definitions, derivations, worked examples, and exam-style problems. Start with thermal properties, then gas laws, then kinetic theory and thermodynamics.