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

2.2.2 Specific Heat Capacity

Learning Objective

Define specific heat capacity as the energy required per unit mass per unit temperature increase and use the equation

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

where c is the specific heat capacity, ΔE is the energy supplied, m is the mass and Δθ is the temperature change.

Definition

Specific heat capacity (c) is the amount of energy (in joules) needed to raise the temperature of 1 kg of a substance by 1 °C (or 1 K).

Units

• SI unit: joule per kilogram per kelvin (J kg⁻¹ K⁻¹)
• Often written as J kg⁻¹ °C⁻¹ because a kelvin and a degree Celsius have the same magnitude.

Derivation of the Equation

Starting from the definition:

\$c = \frac{\text{energy required}}{\text{mass} \times \text{temperature change}}\$

Re‑arranging gives the working form used in calculations:

\$\Delta E = c \, m \, \Delta\theta\$

Typical \cdot alues of Specific Heat Capacity

Worked Example

Problem: How much energy is required to raise the temperature of 250 g of water from 20 °C to 80 °C?

1. Identify the data:

   • Mass, m = 250 g = 0.250 kg
   • Initial temperature, θ₁ = 20 °C
   • Final temperature, θ₂ = 80 °C
   • Temperature change, Δθ = θ₂ − θ₁ = 60 °C = 60 K
   • Specific heat capacity of water, c = 4180 J kg⁻¹ K⁻¹

2. Apply the formula \$\Delta E = c\,m\,\Delta\theta\$:

   \$\Delta E = 4180 \times 0.250 \times 60 = 62\,700\ \text{J}\$

3. Answer: \$6.27 \times 10^{4}\ \text{J}\$ of energy is required.

Common Misconceptions

• Confusing specific heat capacity with heat capacity. Heat capacity (C) refers to the energy needed for a whole object, while specific heat capacity is per unit mass.
• Using the wrong mass unit. Always convert mass to kilograms before using the SI equation.
• Mixing up temperature scales. A change of 1 °C equals a change of 1 K, but the absolute temperature values differ.

Practice Questions

1. A 1.5 kg block of aluminium (c = 900 J kg⁻¹ K⁻¹) is heated from 25 °C to 75 °C. Calculate the energy supplied.
2. How much would the temperature of 500 g of copper (c = 385 J kg⁻¹ K⁻¹) increase if it absorbs 10 kJ of energy?
3. Compare the energy required to raise 1 kg of water and 1 kg of iron (c = 450 J kg⁻¹ K⁻¹) by 10 K. Which requires more energy and why?