Energy changes in systems: mass, m, in kilograms, kg

The idea

In thermal energy calculations, mass m is the amount of substance being heated or cooled, measured in kilograms, kg. The equation ∆E = mc∆θ uses m in kg, so if a mass is given in grams you must divide by 1000 first. For example, 500 g of aluminium is 0.5 kg; heating it by 20 °C with c = 900 J/kg°C gives ∆E = 0.5 × 900 × 20 = 9000 J. Mass is not the same as weight: weight is a force in newtons, while mass in kg measures how much matter is present. In energy calculations, a larger mass needs more energy for the same temperature rise, because more particles must gain kinetic energy. Always identify the mass of the substance that actually changes temperature.

What earns the marks

• States that mass m is measured in kilograms, kg, in the thermal energy equation.
• Converts a mass given in grams to kilograms by dividing by 1000 before substitution.
• Uses m correctly in ∆E = mc∆θ, recognising that a larger mass requires more energy for the same temperature change.
• Distinguishes mass in kg from weight in N, and selects the mass of the substance that changes temperature.
• Rearranges ∆E = mc∆θ to calculate m when ∆E, c and ∆θ are known, giving the answer in kg.

Common mistakes and how to put them right

• Substituting grams directly into the equation.

  Put it right: Convert to kilograms first, for example 250 g = 0.25 kg.

• Confusing mass with weight.

  Put it right: Weight is measured in newtons and depends on gravity, while mass in kg does not.

• Using the mass of the container instead of the mass of the substance whose temperature changes.

Exam tips

• Underline the mass value and its unit in the question, then convert to kg before starting the calculation.
• Show the conversion step, such as 500 g ÷ 1000 = 0.5 kg, so the examiner can follow your reasoning.
• Check that your final answer for m is in kg and is sensible for the context described.