Temperature changes in a system and specific heat capacity: ∆E = m c ∆θ

The idea

This is the symbolic form of the thermal energy equation: ∆E is the change in thermal energy in joules, m is the mass in kilograms, c is the specific heat capacity in joules per kilogram per degree Celsius, and ∆θ is the temperature change in degrees Celsius (or kelvin). The triangle ∆ means 'change in', so ∆θ is final temperature minus initial temperature. For example, a 0.50 kg aluminium block with c = 900 J/kg °C heated from 20 °C to 70 °C has ∆θ = 50 °C, so ∆E = 0.50 × 900 × 50 = 22500 J. Rearranging gives m = ∆E ÷ (c ∆θ), c = ∆E ÷ (m ∆θ) and ∆θ = ∆E ÷ (m c). Use this equation only when the substance stays in the same state; changes of state require specific latent heat instead.

What earns the marks

• Recognise and state that ∆E represents change in thermal energy, m represents mass, c represents specific heat capacity and ∆θ represents temperature change.
• Substitute the given values into ∆E = m c ∆θ, converting mass to kg and temperature change to °C or K as needed.
• Rearrange the equation correctly when the question asks for m, c or ∆θ rather than ∆E.
• Evaluate the expression accurately, keeping track of units and powers of ten.
• State the final answer with the correct unit and a sensible number of significant figures.

Common mistakes and how to put them right

• Treating ∆θ as the final temperature only.

  Put it right by using final temperature minus initial temperature.

• Using grams for mass without converting to kilograms.

  Put it right by dividing grams by 1000 before substituting.

• Confusing c with specific latent heat.

  Put it right by checking whether the question involves a temperature change or a change of state.

Exam tips

• Write the full equation with symbols before substituting numbers, so the meaning of each term is clear.
• When rearranging, do it in steps and check by substituting simple numbers back into the original equation.
• Include the unit J or kJ with the final answer and avoid rounding too early in multi-step calculations.