Thermal capacity measures how much thermal energy a body absorbs per unit temperature rise. Deriving and applying the specific heat capacity equation $c = \Delta E / (m \Delta \theta)$ is essential for thermal engineering and calorimetry in Cambridge IGCSE Physics.

Different materials require different quantities of thermal energy to raise the temperature of a unit mass by one degree.

Definition of Specific Heat Capacity

Specific heat capacity ($c$) is defined as the thermal energy required per unit mass to increase the temperature of a substance by $1^\circ\text{C}$ (or $1\text{ K}$).

Where:

• $\Delta E$ is thermal energy transferred in Joules (J)
• $m$ is mass of the substance in kilograms (kg)
• $\Delta \theta$ is temperature change in $^\circ ext{C}$ or Kelvin (K)
• $c$ is specific heat capacity in $\text{J / (kg }^\circ ext{C)}$

Rearranging gives the thermal transfer equation:

Water possesses an exceptionally high specific heat capacity ($c_{\text{water}} \approx 4200\text{ J/(kg }^\circ\text{C)}$), making it an effective coolant for car engines and power stations. Metals have low specific heat capacities (e.g. $c_{\text{copper}} \approx 390\text{ J/(kg }^\circ\text{C)}$), heating up rapidly when thermal energy is applied.

To measure the specific heat capacity of a metal block in a laboratory:

1. Measure mass $m$ of the metal block on an electronic balance.
2. Insert an electric immersion heater and a digital thermometer into oil-filled holes in the block.
3. Wrap the block in insulating lagging to minimize heat loss to surroundings.
4. Record initial temperature $\theta_1$.
5. Connect heater to a d.c. supply with ammeter and voltmeter. Turn on for time $t$ seconds.
6. Record current $I$, voltage $V$, and final maximum temperature $\theta_2$.
7. Calculate electrical energy supplied: $\Delta E = I V t$.
8. Calculate specific heat capacity:

Advanced Physical Analysis

Evaporation occurs at any temperature below boiling as energetic surface liquid molecules escape into gas, cooling the remaining liquid by removing average kinetic energy.

Extended Experimental Procedures and Quantitative Analysis

Experimental investigations require meticulous measurement and systematic error reduction. Digital timers, micrometers, and vernier calipers reduce uncertainty. Data analysis involves plotting linear graphs, calculating gradients to represent rate of change or physical constants, and comparing experimental values against theoretical expectations to quantify percentage error ($|\text{Exp} - \text{Theo}| / \text{Theo} \times 100\%$).

Specific heat capacity $c = \Delta E / (m \Delta \theta)$ quantifies thermal energy requirements. High $c$ materials like water store large thermal energy with small temperature changes.