Energy changes in systems: ∆E = m c ∆θ

The idea

This is the symbolic form of the thermal energy equation: ΔE is the change in thermal energy in joules, m is the mass in kilograms, c is the specific heat capacity in J/kg °C and Δθ is the temperature change in °C. The triangle Δ means 'change in', so Δθ is final temperature minus initial temperature. To use it, rearrange if necessary, substitute the known values with their units, and calculate.

For example: A 0.5 kg aluminium block (c = 900 J/kg °C) heated by 40 °C gains ΔE = 0.5 × 900 × 40 = 18 000 J. Rearranging gives c = ΔE ÷ (m Δθ), m = ΔE ÷ (c Δθ) and Δθ = ΔE ÷ (m c), which allows any missing quantity to be found.

What earns the marks

• Identify each symbol correctly: ΔE is change in thermal energy in J, m is mass in kg, c is specific heat capacity in J/kg °C and Δθ is temperature change in °C.
• Substitute values into ΔE = m c Δθ with consistent units and evaluate the product.
• Rearrange the equation correctly to make m, c or Δθ the subject when required.
• Interpret Δθ as final temperature minus initial temperature and apply it to heating or cooling situations.
• Give the final answer with the correct unit and an appropriate number of significant figures.
• Use the equation to compare energy transfers for equal masses of different materials with different specific heat capacities.

Common mistakes and how to put them right

• Treating Δθ as the final temperature only.

  Put it right: Subtract the initial temperature from the final temperature.

• Using inconsistent units, such as grams with J/kg °C.

  Put it right: Convert mass to kg first.

• Rearranging incorrectly, for example dividing by m c when finding Δθ instead of dividing ΔE by m c.

Exam tips

• Write the rearranged equation before substituting numbers, especially when the question asks for c, m or Δθ.
• Include units throughout the substitution line to show that the final unit is joules.
• If the answer is large, convert to kJ or MJ only if the question asks for it, and keep the unit clear.