Energy changes in systems: specific heat capacity, c, in joules per kilogram per degree Celsius, J/kg °C

The idea

Specific heat capacity, c, is the energy needed to raise the temperature of 1 kg of a substance by 1 °C. Its unit, J/kg °C, shows this: joules of energy per kilogram of material per degree Celsius of temperature rise. For example, water has c = 4200 J/kg °C, so heating 2 kg of water by 10 °C needs E = mc∆θ = 2 × 4200 × 10 = 84 000 J. A low c means the substance warms quickly for a given energy input; a high c means it warms slowly. You use c in E = mc∆θ, rearranged as c = E ÷ (m∆θ), and you must keep mass in kg and temperature change in °C so the unit comes out as J/kg °C.

What earns the marks

• State that specific heat capacity is the energy required to raise the temperature of 1 kg of a substance by 1 °C.
• Use the unit J/kg °C correctly, recognising it means joules per kilogram per degree Celsius.
• Substitute values into E = mc∆θ with mass in kg, temperature change in °C and c in J/kg °C.
• Rearrange c = E ÷ (m∆θ) correctly when asked to calculate specific heat capacity.
• Interpret a high c as a large energy input for a given temperature rise, and a low c as a small energy input.
• Compare values of c to explain why some materials heat up or cool down faster than others.

Common mistakes and how to put them right

• Using mass in grams instead of kilograms.

  Put it right: Convert grams to kilograms by dividing by 1000 before substituting into E = mc∆θ.

• Confusing specific heat capacity with specific latent heat.

  Put it right: c applies to a temperature change with no change of state, while latent heat applies to a change of state at constant temperature.

• Writing the unit as J/kg or J/°C only.

  Put it right: The correct unit is J/kg °C because it includes both mass and temperature change.

Exam tips

• Write the equation E = mc∆θ, then substitute values with units before calculating so errors in mass or temperature are easier to spot.
• Check that the temperature change is a rise or fall by subtracting the initial temperature from the final temperature, not by adding them.
• When comparing materials, quote the c values and link the larger c to the smaller temperature change for the same energy input.