Define specific heat capacity as the energy required per unit mass per unit temperature increase; recall and use the equation c = ΔE / m Δθ

What is Specific Heat Capacity?

Specific heat capacity, denoted by \$c\$, is the amount of energy required to raise the temperature of 1 kg of a substance by 1 °C (or 1 K). It tells us how “slow” or “fast” a material heats up.

The Equation

\$c = \dfrac{\Delta E}{m\,\Delta\theta}\$

Where:

• \$\Delta E\$ = energy added (J)
• \$m\$ = mass of the substance (kg)
• \$\Delta\theta\$ = change in temperature (°C or K)

Analogy: The “Heat Sponge”

Imagine a sponge that can soak up water. A material with a high specific heat (like water) is a “big sponge” – it can absorb a lot of energy before its temperature rises. A material with a low specific heat (like metal) is a “tiny sponge” – it heats up quickly.

Example

Suppose 0.5 kg of copper (specific heat \$c_{\text{Cu}} = 0.385\,\text{J g}^{-1}\text{K}^{-1} = 385\,\text{J kg}^{-1}\text{K}^{-1}\$) is heated by 50 °C. How much energy is required?

Exam Tips 🚀

1. Always check units – \$c\$ is usually given in J kg⁻¹ K⁻¹ or J g⁻¹ K⁻¹. Convert if necessary.
2. Remember that Δθ is the final temperature minus the initial temperature.
3. When the problem asks for energy, rearrange the equation: ΔE = c m Δθ.
4. For “heat lost” problems, use a negative sign for ΔE.
5. Practice quick mental conversions: 1 kJ = 1000 J, 1 g = 0.001 kg.

Quick Summary

Specific heat capacity tells us how much energy is needed to change a material’s temperature. Use the formula \$c = \Delta E/(m\,\Delta\theta)\$ or its rearranged form \$\Delta E = c\,m\,\Delta\theta\$ to solve problems.