$$Q = mc\Delta\theta \qquad \text{Heat capacity } C = mc = \frac{Q}{\Delta\theta}$$ $c$ = specific heat capacity (J/kg K), $\Delta\theta$ = temperature change.

Latent heat (change of state, no temperature change)

$$Q = mL \qquad L_f = \text{specific latent heat of fusion}, \quad L_v = \text{specific latent heat of vaporisation}$$

Heat exchange

Heat lost by the hot body $=$ heat gained by the cold body: $\ m_1c_1(\theta_1 - \theta) = m_2c_2(\theta - \theta_2)$.

Electrical heating

$$\text{Electrical energy} = Pt = VIt = mc\Delta\theta \ (\text{no losses}) \qquad \text{with a latent change: } Pt = mL$$

Expansion

$$\text{Linear: } \Delta L = \alpha L_0 \Delta\theta \qquad \text{Area: } \Delta A = \beta A_0\Delta\theta \qquad \text{Volume: } \Delta V = \gamma V_0\Delta\theta$$

Thermometers

$$\text{Temperature} = \frac{X_\theta - X_0}{X_{100} - X_0}\times 100^\circ\text{C}$$