(a) specific heat capacity of a substance; the equation E = mcΔθ

The idea

Specific heat capacity c is the energy needed to raise the temperature of 1 kg of a substance by 1 K, measured in J kg⁻¹ K⁻¹. The energy transferred for a temperature change is E = mcΔθ, where m is mass in kilograms and Δθ is the temperature change in kelvin or degrees Celsius.

For example: Heating 0.50 kg of aluminium (c = 900 J kg⁻¹ K⁻¹) by 20 K needs E = 0.50 × 900 × 20 = 9.0 × 10³ J. A question may ask for the definition, the unit, or a value of E, m, c or Δθ.

What earns the marks

• Specific heat capacity is the energy needed to raise the temperature of 1 kg of a substance by 1 K.
• The unit of specific heat capacity is J kg⁻¹ K⁻¹.
• The equation E = mcΔθ relates energy transferred, mass, specific heat capacity and temperature change.
• Mass must be in kilograms and Δθ is the temperature change in kelvin or degrees Celsius.
• A temperature difference in kelvin equals the same difference in degrees Celsius.

Common mistakes and how to put them right

• Using mass in grams instead of kilograms.

  Put it right: Convert grams to kilograms by dividing by 1000 before substituting.

• Using the final temperature instead of the temperature change.

  Put it right: Δθ is the difference between final and initial temperatures.

• Confusing specific heat capacity with specific latent heat.

  Put it right: Specific heat capacity applies to a temperature change, not a phase change.

• Writing the unit as J kg⁻¹ °C⁻¹ only.

  Put it right: J kg⁻¹ K⁻¹ is the standard unit, and a temperature difference in kelvin equals one in degrees Celsius.

Exam tips

• Write down E = mcΔθ, rearrange for the unknown, then substitute values with units.
• Convert mass to kilograms and check whether the question gives a temperature change or two temperatures.
• Check the magnitude of your answer: a small temperature change of a small mass should give a modest energy value.