PURPOSE

To study the varying property of different substances to absorb heat through the method of mixtures, i.e., placing a hot body in thermal contact with a cold body to determine the final equilibrium temperature.

EQUIPMENT

Bunsen burner with ring stand, double boiler, 2 thermometers, simple double-walled calorimeter, metal (Pb) shot, pan balance, drying tray.

RELEVANT EQUATIONS

DISCUSSION

From experience, it is known that when heat Q is applied to any body, the temperature will rise in direct proportion as long as no change of phase is taking place. The constant of proportionality C, is called the heat capacity of the body. We can write down the following relationship between the heat applied Q, and the temperature change DT.

In the metric system, heat is usually measured in calories or joules, and temperature change in degrees Celsius. The calorie is defined in terms of the thermal properties of water. One calorie is the amount of heat required to raise the temperature of one gram of water by one degree Celsius. Notice how the mass of water enters into this definition. It is observed that the heat capacity of any substance will depend upon the mass of the object under study. In fact, the heat capacity is directly proportional to the mass of the object. In order to derive a quantity that is a useful measure of the thermal properties of a substance in general, we divide the heat capacity C by the mass m of the body under study to obtain the specific heat c:

We can get a value for the specific heat of a substance by applying some heat, measuring the resulting rise in temperature, and dividing by it and the mass of the body.
 

Rearranging to find the heat added or removed:

 where c is measured in units of: , or . Since a temperature change of 1 C° is the same as a change of 1 K, a kilogram = 1000 grams, and there are 4.186 joules in a calorie, the conversion between these units is:

In this experiment, you will measure the specific heat of a pure metal by using the method of mixtures. In this method, a hot body is placed in thermal contact with a cold body, usually a quantity of cold water kept in an insulated container called a calorimeter. The two bodies are brought together in the calorimeter so that no heat is gained from or lost to the surroundings. Eventually, the entire system reaches some intermediate temperature between that of the hot body and that of the cold body. Using this assumption, and the law of conservation of energy, we can write an equation which expresses the fact that the heat lost by the hot body is equal to the heat gained by the cold one.

If T_h is the original temperature of the hot metal, T_f is the final equilibrium temperature, and T_c is the original temperature of the cold cup, water and stirrer, then we can use the relationship between heat, mass, temperature change and specific heat to write:

 In this equation, the subscripts refer to the various parts of the real system: mis for the metal; wis for the water; and,csis for the cup and stirrer (assumed to be made of the same substance). One can therefore determine the specific heat of the metal shot by measuring the initial and final temperatures of the hot and the cold bodies, and their masses, assuming that the specific heat of water and of the cup-stirrer material is known. The specific heat of the metal can be calculated by using:

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