Energy changes in systems: The amount of energy stored in or released from a system as its temperature changes can be calculated using the equation:

The idea

When a system is heated or cooled, energy is transferred to or from its thermal store. The energy change depends on the mass of the substance, its specific heat capacity and the temperature change. The equation is ΔE = m c Δθ, where ΔE is the energy change in joules (J), m is mass in kilograms (kg), c is specific heat capacity in joules per kilogram per degree Celsius (J/kg°C), and Δθ is the temperature change in degrees Celsius (°C). For example, heating 2 kg of water (c = 4200 J/kg°C) by 10°C transfers ΔE = 2 × 4200 × 10 = 84 000 J. If the temperature falls, the same equation gives the energy released. Always find Δθ by subtracting the initial temperature from the final temperature, and convert grams to kilograms before substituting.

What earns the marks

• The equation ΔE = m c Δθ calculates energy transferred to or from a thermal store during a temperature change.
• ΔE is measured in joules (J), m in kilograms (kg), c in joules per kilogram per degree Celsius (J/kg°C), and Δθ in degrees Celsius (°C).
• Δθ is the temperature change, calculated as final temperature minus initial temperature.
• Specific heat capacity is the energy needed to raise the temperature of 1 kg of a substance by 1°C.
• A temperature decrease gives the same numerical energy change as the equivalent increase, representing energy released rather than stored.
• Mass must be in kilograms; 500 g becomes 0.5 kg before substitution.

Common mistakes and how to put them right

• Using the final temperature instead of the temperature change.

  Put it right by subtracting the initial temperature from the final temperature.

• Substituting mass in grams.

  Put it right by dividing by 1000 to convert to kilograms.

• Mixing up the units of specific heat capacity.

  Put it right by checking that c is in J/kg°C and that the temperature change is in °C.

Exam tips

• Write the equation, then list m, c and Δθ with their values and units before calculating.
• If a temperature falls, still use a positive Δθ and state that energy is released.
• Check that the answer is in joules and that the size of the answer is sensible for the mass and temperature change given.