Energy changes in systems: change in thermal energy = mass × specific heat capacity × temperature change

The idea

This equation links the energy transferred to a substance to its mass, its specific heat capacity and the temperature rise or fall. Specific heat capacity is the energy needed to raise 1 kg of a substance by 1 °C, so a large value means the substance stores a lot of energy for a small temperature change. To use the equation, identify the mass in kilograms, the specific heat capacity in J/kg °C and the temperature change in °C, then multiply.

For example: Heating 2 kg of water (c = 4200 J/kg °C) by 30 °C transfers 2 × 4200 × 30 = 252 000 J. The same equation gives the energy released when a substance cools, because temperature change is the difference between the final and initial temperatures.

What earns the marks

• State the equation as change in thermal energy = mass × specific heat capacity × temperature change and use the correct symbols ΔE = m c Δθ.
• Convert mass to kilograms and express temperature change in °C before substituting values.
• Substitute numerical values correctly, including the specific heat capacity in J/kg °C, and evaluate the product accurately.
• Give the answer in joules (J) and, where appropriate, convert to kilojoules by dividing by 1000.
• Explain that specific heat capacity is the energy required to raise the temperature of 1 kg of a substance by 1 °C.
• Rearrange the equation to find mass, specific heat capacity or temperature change when the other quantities are known.

Common mistakes and how to put them right

• Using the final temperature instead of the temperature change.

  Put it right: Calculate Δθ as final temperature minus initial temperature, and keep the sign meaningful for heating or cooling.

• Forgetting to convert grams to kilograms.

  Put it right: Divide a mass in g by 1000 before substituting, because specific heat capacity is given per kilogram.

• Mixing up specific heat capacity with specific latent heat.

  Put it right: Use c for temperature changes with no change of state, and latent heat only during melting or boiling.

Exam tips

• Write the equation, then substitute values with units before calculating, so method marks can be awarded even if the final arithmetic slips.
• Check that the temperature change is in °C and the mass is in kg; these are the units expected by the specific heat capacity value.
• For a cooling question, calculate the temperature fall as initial minus final and state that the energy is transferred away from the substance.