Temperature and Thermal Properties of Matter

Temperature & Energy

Temperature is not a substance, but a census: the average kinetic energy of microscopic molecules. Temperature measures this average kinetic energy, while heat is energy transferred strictly due to a temperature difference.

Common pitfall: Temperature and heat are distinct. A 1000 degree sparkler holds far less thermal energy than a 40 degree bathtub because heat depends on total molecular count.

Temperature scales convert via:

$T_K = T_C + 273.15$

$T_F = \frac{9}{5}T_C + 32$

Thermal expansion causes materials to grow when heated, tracked by linear and volume formulas:

$\Delta L = \alpha L_0 \Delta T$

$\Delta V = \beta V_0 \Delta T$

Here, $\beta \approx 3\alpha$, representing the expansion coefficients.

Heat & Phase Changes

Heat capacity determines energy needed to shift temperature via $Q = mc\Delta T$.

Phase changes occur at constant temperature using $Q = mL$, where $L$ is latent heat of fusion or vaporisation.

Calorimetry in isolated systems dictates heat lost equals heat gained:

$\sum Q_i = 0$

$m_1 c_1(T_f - T_1) + m_2 c_2(T_f - T_2) = 0$

Tip: Always check for phase changes before applying $Q = mc\Delta T$. At melting or boiling points, account for latent heat first.