Temperature and Thermal Properties of Matter

Temperature is not a substance but a census: the average kinetic energy of molecules too small to see. Once you buy that, thermal phenomena become mechanics — expansion is atoms jostling for elbow room, and the absolute zero of temperature is simply the floor where jostling stops.

Temperature measures the average kinetic energy of molecules. Heat is energy transferred due to a temperature difference.

Temperature scales

$$T_K = T_C + 273.15, \qquad T_F = \frac{9}{5}T_C + 32$$

Thermal expansion — Most materials expand when heated:

$$\Delta L = \alpha L_0 \Delta T \quad\text{(linear)}, \qquad \Delta V = \beta V_0 \Delta T \quad\text{(volume)}$$

where $\beta \approx 3\alpha$.

Heat capacity — The energy needed to raise the temperature:

$$Q = mc\Delta T$$

Phase changes occur at constant temperature:

Q = mL

where $L$ is the latent heat (of fusion or vaporisation).

Calorimetry — In an isolated system, heat lost = heat gained:

$$\sum Q_i = 0 \implies m_1 c_1(T_f - T_1) + m_2 c_2(T_f - T_2) = 0$$

Tip: Always check whether a phase change occurs before assuming $Q = mc\Delta T$. If the system reaches $0^{\circ}$C or $100^{\circ}$C, account for latent heat.

Common pitfall: Temperature and heat are different currencies. A sparkler at 1000 °C holds far less thermal energy than a bathtub at 40 °C — temperature is the average per molecule; heat depends on how many molecules are paying in.