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Physics

Heat in the home

Specific heat capacity and calculating heat energy

When you supply heat energy to a substance, you cause its temperature to increase. The change in temperature of the substance depends on the mass of the substance and the quantity of heat that is supplied to it. The change in temperature that is produced also depends on a property of the material called its specific heat capacity.

The specific heat capacity, c, is the heat energy that is needed to raise the temperature of a specific mass of the substance, namely 1 kg, through 1 degree celsius. Specific heat capacity is measured in joules per kilogram degree celsius (J/kg °C).

The heat energy Eh which has to be supplied to a substance of mass m and specific heat capacity c to raise its temperature by ΔT is given by the following relationship.

Eh = c m ΔT

  • Eh is measured in joules
  • m is measured in kilograms
  • ΔT is measured in °C
  • c is measured in joules/kg °C

The same relationship can be used to calculate the heat that is given out by a substance as it cools.

Your are expected to be able to use this relationship in calculating the heat gained, or the heat lost by a substance.

Here is a typical examination question. Try the question and test your ability to use the relationship for heat gained or heat lost by a substance. Then click on 'reveal solution' and 'next step' to see how you got on.

Question

1 An electric heater supplies 13500 joules of heat energy to a metal block of mass 0.5 kg. The temperature of the block rises from 20 °C to 80 °C during the heating process. Assuming that very little heat is lost from the block during the heating process, what is the specific heat capacity of the metal?

Answer

In order to calculate the specific heat capacity of the metal you need to take the following steps:

\eqalign{ m & = & 0.5kg \cr \cr \Delta\;T & = & (80-20) \cr \cr &=& 60^oC \cr \cr \cr Heat\; gained,\;E_h & = & c\;m\;\Delta\;T \cr \cr c &=& {E_h \over m \Delta\;T} \cr \cr &=& {13500 \over (0.5 \times 60)} \cr \cr &=& 450\cr}

specific heat capacity of the metal = 450 J/kg °C

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What a scorcher! Video clip about heat transfer.

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