Specific Heat Capacity

Different materials warm up at different speeds. Heating adds energy to a substance, increasing its internal energy because its particles move faster. Specific heat capacity explains how much energy is needed to change temperature.

Definition and equation

• Specific heat capacity (c) is the energy needed to raise the temperature of 1 kg of a material by 1°C (or 1 K).
• Units: J/(kg °C) or J/(kg K).
• Energy and temperature change are linked by: $$Q = mc\Delta\theta$$ where Q is energy (J), m is mass (kg), c is specific heat capacity, and $\Delta\theta$ is temperature change (°C or K).
• Rearrange if needed: $c = \dfrac{Q}{m\Delta\theta}$, $\Delta\theta = \dfrac{Q}{mc}$.

Understanding c

• High c means a material needs lots of energy to warm up and cools down slowly (like water).
• Low c means it warms quickly and cools quickly (many metals).
• Temperature tells how hot something is, but energy stored also depends on mass and the material.

Measuring c (simple experiments)

Solid (electrical heating method)

1. Find the mass m of the solid. Insert a heater and thermometer; wrap in insulation.
2. Record starting temperature. Switch on the heater: measure voltage V, current I, and time t.
3. Energy supplied: $Q = VIt$. Temperature rise: $\Delta\theta$.
4. Calculate $c = \dfrac{VIt}{m\Delta\theta}$.

Liquid

1. Put the liquid in an insulated calorimeter with a lid and a stirrer; measure the liquid’s mass.
2. Use an immersion heater and thermometer. Measure V, I, and t while stirring gently.
3. Use $Q = VIt$ and $c = \dfrac{Q}{m\Delta\theta}$. Some energy heats the container, so good insulation reduces error.

Real-world links

• Water (high c) helps cool car engines and keeps coastal climates mild.
• Cookware: metal pans heat fast; handles use materials with higher c or low conductivity to stay cooler.

Common mistakes

• Using grams instead of kilograms in the formula.
• Thinking temperature rise alone tells energy; mass and c matter.
• Ignoring heat losses; always insulate and use a lid.

Key points

• c is energy per kg per degree.
• $$Q = mc\Delta\theta$$ and for electrical heating $Q = VIt$.
• High c materials warm and cool slowly.