Specific heat capacity and specific latent heat

Physics A2 · Temperature. The idea in plain words, the rules to remember, the mistake to avoid and a worked example, written and checked by Mega Lecture.

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The idea

Supplying thermal energy to a substance can do one of two things. It can raise the temperature, or it can change the state at constant temperature.

Specific heat capacity c is the energy needed per unit mass to raise the temperature by one degree. Specific latent heat L is the energy needed per unit mass to change the state with no change of temperature: fusion for solid to liquid, vaporisation for liquid to gas.

During a change of state the energy increases the potential energy of the molecules, not their kinetic energy, so the temperature stays constant. Vaporisation needs much more energy than fusion, because the molecules are separated completely and the vapour must push back the atmosphere.

Rules to remember

Common mistake

Students use mcΔθ during melting or boiling, where Δθ = 0. Split the problem into stages: mL for each change of state and mcΔθ for each temperature change, then add. Change grams to kilograms.

Worked example

A 50 W heater is used for 180 s to heat an insulated aluminium block of mass 0.40 kg. The specific heat capacity of aluminium is 900 J kg−1 K−1. What is the rise in temperature?

  1. Energy supplied: E = Pt = 50 × 180 = 9000 J.
  2. Rearrange E = mcΔθ: Δθ = E ÷ (mc).
  3. Δθ = 9000 ÷ (0.40 × 900) = 9000 ÷ 360 = 25 K.

Answer: A rise of 25 K (25 °C).

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