SPECIFIC HEAT
 

Pure liquid water requires 1 calorie per gram (1 cal/g) to warm it up or cool it down by 1°C (provided it is not at the melting/freezing temperature or the vaporization/condensation temperature, as we shall shortly see.) However, what about oil, alcohol, or salt water? What about solids such as steel or wood? What about gases such as air? It is not so simple then. A certain, fixed amount of heat energy will raise or lower the temperatures of fixed masses of some substances more than others. Some matter takes more than 1 cal/g to get hotter or cooler by 1°C; some matter takes less. Pure liquid water takes exactly 1 cal/g to warm up or cool down by 1°C simply because this is the substance on which the definition of the calorie is based. It is one of those things scientists call a convention.
Suppose that we have a sample of some mysterious liquid. Call it substance X. We measure out 1 gram (1.00 g), accurate to three significant figures, of this liquid by pouring some of it into a test tube placed on a laboratory balance. Then we transfer 1 calorie (1.00 cal) of energy to substance X. Suppose that, as a result of this energy transfer, substance X increases in temperature by 1.20°C? Obviously, substance X is not water because it behaves differently from water when it receives a transfer of energy. In order to raise the temperature of 1.00 g of this stuff by 1.00°C, it takes somewhat less than 1.00 cal of heat. To be exact, at least insofar as we are allowed by the rules of significant figures, it will take 1.00/1.20 = 0.833 cal to raise the temperature of this material by 1.00°C.

Now suppose that we have a sample of another material, this time a solid. Let’s call it substance Y. We carve a chunk of it down until we have a piece that masses 1.0000 g, accurate to five significant figures. Again, we can use our trusty laboratory balance for this purpose. We transfer 1.0000 cal of energy to substance Y. Suppose that the temperature of this solid goes up by 0.80000°C? This material accepts heat energy in a manner different from either liquid water or substance X. It takes a little more than 1.0000 cal of heat to raise the temperature of 1.0000 g of this material by 1.0000°C. Calculating to the allowed number of significant figures, we can determine that it takes 1.0000/0.80000 = 1.2500 cal to raise the temperature of this material by 1.0000°C.
We’re onto something here: a special property of matter called the specific heat, defined in units of calories per gram per degree Celsius (cal/g/°C). Let’s say that it takes c calories of heat to raise the temperature of exactly 1 gram of a substance by exactly 1°C. For water, we already know that c = 1 cal/g/°C, to however many significant figures we want. For substance X, c = 0.833 cal/g/°C (to three significant figures), and for substance Y, c = 1.2500 cal/g/°C (to five significant figures).
Alternatively, c can be expressed in kilocalories per kilogram per degree Celsius (kcal/kg/°C), and the value for any given substance will be the same. Thus, for water, c = 1 kcal/kg/°C, to however many significant figures we want. For substance X, c=0.833 kcal/kg/°C (to three significant figures), and for substance Y, c = 1.2500 kcal/kg/°C (to five significant figures).

مواضيع ذات صلة

الديناميكا الحرارية الجزيئية

توزيع بولتزمان

العلاقات بين الخواص

القانون الثالث للديناميكا الحرارية

الطاقة الحرة

القانون الثاني للديناميكا الحرارية

القانون الأول للديناميكا الحرارية

Order and entropy

Irreversibility

The Clausius-Clapeyron equation

Internal energy

Entropy