Know that a rise in the temperature of an object increases its internal energy

2.2.2 Specific Heat Capacity

What is Specific Heat Capacity?

Specific heat capacity ($c$) is the amount of heat energy needed to raise the temperature of 1 kg of a substance by 1 °C (or 1 K). It tells us how “slowly” or “quickly” an object’s temperature changes when we add heat.

Formula

$$Q = m\,c\,\Delta T$$

Where:

• $Q$ = heat added (J)
• $m$ = mass (kg)
• $c$ = specific heat capacity (J kg⁻¹ K⁻¹)
• $\Delta T$ = change in temperature (K)

Why Does Temperature Rise Increase Internal Energy?

When you add heat to an object, the energy goes into increasing the kinetic energy of its molecules. More kinetic energy means a higher average speed → higher temperature. That extra kinetic energy is part of the object’s internal energy.

Analogy: The Hot Water Bottle

Imagine a hot water bottle. If you fill it with warm water and then put it in a cold room, the water’s temperature will drop. The bottle’s internal energy decreases because the water molecules slow down. The same idea works when you heat something: the molecules speed up, raising the internal energy.

Examples

1. Heating 0.5 kg of water from 20 °C to 80 °C: $Q = 0.5\,\text{kg}\times 4184\,\text{J kg⁻¹ K⁻¹}\times 60\,\text{K} = 1.26\times10^5\,\text{J}$.
2. Heating 0.2 kg of iron from 20 °C to 120 °C: $Q = 0.2\times 449\,\times 100 = 8.98\times10^3\,\text{J}$.

Table of Common Substances

Quick Check

• What happens to $Q$ if you double the mass but keep $\Delta T$ the same?
• Why does water have a higher $c$ than iron?

Key Takeaway

Increasing the temperature of an object by adding heat increases its internal energy because the molecules move faster. The specific heat capacity tells us how much heat is needed for a given temperature rise.