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Measurement of Thermal Energy

12 min read

Heat capacity

Heat is a form of energy measured in joules. The amount of heat needed to raise the temperature of an object depends on its mass, the temperature rise and the material. The heat capacity C of an object is the heat needed to raise its temperature by 1 K (J/K). The specific heat capacity c of a material is the heat needed to raise the temperature of 1 kg by 1 K (J kg⁻¹ K⁻¹).

Q = heat gained or lost, m = mass, c = specific heat capacity, ΔT = change in temperature.
  • specific heat capacity (J kg⁻¹ K⁻¹)
Water has a very high specific heat capacity: it takes a lot of heat to warm it and it stays warm for a long time. That is why the sea is cooler than the land by day.
Try itHeating a substance

Choose the mass, the material (specific heat capacity) and the temperature rise. Find the heat needed.

Worked exampleHeating water

How much heat is needed to raise the temperature of 3 kg of water from 20 °C to 80 °C? (c = 4 200 J/(kg K))

  1. ΔT = 60 K.

Answer: The heat needed is 756 000 J (756 kJ).

Method of mixtures

When a hot object is placed in cooler water, heat flows from the hot object to the water until they reach the same temperature. If no heat is lost to the surroundings, heat lost by the hot object = heat gained by the cold object. This lets us find an unknown specific heat capacity.

Worked exampleFinding c of a metal

0.20 kg of a metal at 100 °C is put into 0.40 kg of water at 20 °C. The final temperature is 25 °C. Find the specific heat capacity of the metal. (c of water = 4 200)

  1. Heat gained by the water.
  2. Heat lost by the metal (ΔT = 75 K).

Answer: The metal has c = 560 J/(kg K).

Change of state: latent heat

When a substance changes state, heat is taken in or given out without a change in temperature. This is latent heat. The specific latent heat of fusion l_f is the heat needed to change 1 kg of solid to liquid at its melting point. The specific latent heat of vaporisation l_v is the heat needed to change 1 kg of liquid to gas at its boiling point.

For water: l_f = 334 000 J/kg and l_v = 2 260 000 J/kg. A lot more heat is needed to boil water than to melt ice, because the particles must be separated completely.
Heating curve of waterA graph of temperature against time as ice is heated. The line rises while ice warms, stays flat at 0 degrees while it melts, rises again as liquid water warms, stays flat at 100 degrees while it boils, then rises as steam warms.time (heat added)temperature (°C)0100ice warmsmeltingwater warmsboilingsteamtemperature stays at 0 °Cstays at 100 °C
Try itMelting and boiling

Choose the mass of ice at 0 °C. Find the heat to melt it, then to warm it to 100 °C and boil it all away.

Check yourself Which has the highest specific heat capacity?
Check yourself Heat needed to melt 2 kg of ice at 0 °C (l_f = 334 kJ/kg)…
Check yourself During melting, the temperature of a pure substance…

Key terms

Specific heat capacity
The heat needed to raise the temperature of 1 kg of a material by 1 K.
Latent heat
Heat absorbed or released during a change of state without a change of temperature.
Calorimeter
A container used to measure heat transfers.
Heat capacity
The heat needed to raise the temperature of an object by 1 K.

Summary

  • Q = mcΔT; heat capacity C = mc.
  • Method of mixtures: heat lost = heat gained.
  • Latent heat Q = ml: heat is absorbed or released without a temperature change.
  • Water has a high specific heat capacity and large latent heats.
Transfer of Thermal Energy Vapour and Humidity