Heat Capacity

If you heat water, the temperature goes up. You could use fire or electricity to do the heating. When heat energy is transferred to the water, it warms up. So how much energy is needed to warm 1 kg of water by 1 degree Celsius? The answer is 4200 J. If we need to heat a lot of water, we need a lot of energy. This could be expensive.

Heat capacity is useful to help estimate the energy needed to warm, or cool, a substance. The heat capacity of copper, for instance, would be different. To warm 1 kg of copper by 1 degree Celsius, we need 385 J of heat. If we heat water in a copper kettle, we need to supply some heat to the kettle as well, but hopefully not too much.

How do we measure heat capacity? The heat capacity is the amount of heat needed to raise the temperature of a substance by 1 degree Celsius. We need:

  1. A sample of the substance, e.g. cup of water.
  2. A thermometer to measure the temperature.
  3. A method to measure the heat supplied.

The last is the most tricky. If we use fire, there is no simple way to know how many Joules of heat from the fire goes into the water. One easy way is to use electricity. To set up the experiment:

  1. We need a heating element. This is a piece of wire that heats up when electric current passes.
  2. We need a voltmeter to measure the voltage V across the element, and
  3. an ammeter to measure the current I through it.
  4. We also need a power supply to supply this electric current, and
  5. a stop watch to measure the time.

I shall explain on another page, how to connect these together. Assume for now that we have collected together these items, either from a school laboratory, or a shop of scientific instruments. The rate P at which heat is produced by the heating element is P = VI, where V is the voltage and I the current. We can read off V and I from the meters and calculate P. This tells us how many Joules of heat is released to the water every second.

Use the stop watch to measure the time t for the thermometer reading to go up by 1 degree. The heat energy Q is then power x time = Pt. So heat capacity C = Q = Pt = VIt.

Heat capacity is the heat needed to raise the temperature of a substance by 1 degree Celsius. A related quantity is the specific heat capacity, c. This is the heat capacity of 1 kg of the substance. So c = C/m, where m is the mass of the substance.

Copyright 2010 by Kai Hock. All rights reserved.
Last updated: 17 October 2010.