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Ways to Measure Heat Capacity

A certain amount of energy will heat a kettle of water from room temperature to boiling. The same amount applied to an entire bathtub full of water will raise the temperature by no more than a few degrees. The heat capacity -- the amount of heat energy required to raise the temperature of an object by a specific amount -- is directly proportional to the mass of the object. It also depends on a physical property of the substance called specific heat. The amount of energy required to heat a gram of gold by one degree will not raise a gram of water by one degree. Water has a higher specific heat.

Specific Heat
- Specific heat is an intrinsic property of a substance and is independent of its mass. It is the amount of energy required to raise the temperature of a specific mass of the substance by one degree Celsius, and is usually expressed in joules per gram. Gold has a specific heat of .129, while water's specific heat is 4.179.
Heat Capacity
- There is a very simple relationship between heat capacity and specific heat. The specific heat multiplied by the mass, in grams, is the heat capacity. The heat capacity of one kilogram of water is 4179 joules/degrees Celsius. It's a simple matter to look up the specific heat of any known substance, measure its mass, and calculate its heat capacity. If you don't know what the substance is and need to measure it directly, this will require more effort.
Measurement
- To determine the heat capacity or specific heat of an unknown substance, all you need to do is measure the mass of the substance, add heat energy to it, measuring how much heat you are adding, and then measure the amount by which the temperature rises. Measuring the mass and change in temperature are very simple. Determining exactly how much heat is added to the system is a more challenging problem. You can't use your Bunsen burner, because you don't know how many joules of energy it produces, and how much is lost to the air. You need a precise and accurate way to measure exactly how much heat is required to raise your substance by a specific number of degrees.
Electricity
- Power is energy over time, and one watt is equal to one joule per second. Power in an electric circuit is also equal to the product of amperage and voltage. If you heat your substance with a heating element in an electric circuit equipped with an ammeter and a voltimeter, you can determine the amount of power, in watts, by multiplying amperage times voltage. Record the number of seconds necessary to raise the temperature of the substance by one degree Celsius. Multiply this amount of time by the power, and you will have the amount of energy used, which is the heat capacity of your sample. Remember that heat capacity is dependent on the mass of the subject. Divide by the mass, in grams, to determine the specific heat of the substance.
Water
- Another approach uses a known heat capacity to measure an unknown. A kilogram of water has a heat capacity of 4179 joules/degrees Celsius. Record the temperature of a kilogram of water. Add a known mass of another substance at a higher temperature and wait until the temperature has come to an equilibrium and record the change in temperature. Use a well-insulated container, or you will lose heat and accuracy. Suppose the final equilibrium temperature is 10 degrees higher than the water was at the beginning. You know that the new substance must have imparted 41,790 joules to the water, and lost this much itself. Divide 41,790 by the change in temperature of the new substance in degrees Celsius and you'll have the substance's heat capacity. Divide by mass to get specific heat.

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