Specific Heat

1868 j 3 1 23 heat capacity the heat capacity c of an

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Unformatted text preview: ometimes called the Calorie (Cal) is really a kilocalorie.) The relations among the heat units are: 1 cal = 4.1868 J 3 (1) 2.3 Heat Capacity The heat capacity C of an object is the proportionality constant between the heat Q that the object absorbs or loses and the resulting temperature change ΔT of the object: that is ∆ (2) (3) ∆ in which Ti and Tf are the initial and final temperatures of the object. Heat capacity C has the unit of energy per degree or energy per Kelvin. The heat capacity C of, say, a marble slab used in a bun warmer might be 179 cal/°C, which we can write as 179 cal/K or as 749 J/K. The word “capacity” in this context is really misleading in that it suggests analogy with the capacity of a bucket to hold water. That analogy is false, and you should not think of the object as “containing” heat or being limited in its ability to absorb heat. Heat transfer can be proceed with limit as long as the necessary temperature difference is maintained. The object may, of course, melt or vaporize during the process. 2.4 Specific Heat Two objects made of the same material—say, marble—will have heat capacities proportional to their masses. It is therefore convenient to define a “heat capacity per unit mass” or specific heat c that refers not to an object but to a unit mass of the material of which the object is made. Thus equation (2) becomes ∆ (4) (5) ∆ Through experiment we would find that although the heat capacity of a particular marble slab might be 179 cal/°C (or 749 J/K), the specific heat of the marble itself is 0.21 cal/ g·°C (or 880 J/kg·K). Thus we can define the specific heat of water as C=1 cal/ g·°C = 4190 J/ kg·K (6) 2.5 An Important point In determining and using the specific heat of any substance, we need to know the conditions under which energy is transferred as heat. For solids and liquids, we usually assume that the sample is under constant pressure (usually atmospheric) during the transfer. It is also conceivable that the sample is held at constant volume while the heat is absorbed. This means that the thermal expansion of the sample is prevented by applying external pressure. For solids and liquids, this is very hard to arrange experimentally, but the effect can be calculated, and it turns out that the specific heats under constant pressure and constant volume for any solid or liquid differ usually by no more than a few percent. Gases have quite different values for their specific heats under constant pressure conditions under constantvolume conditions. 2.6 Heats of Transformations When energy is absorbed as heat by a solid or liquid, the temperature of the sample does not necessarily rise. Instead, the sample may change from one phase, or state, to another. Matter can exist in three common states: In the solid state, the molecules of a sample are locked into a fairly rigid structure by their mutual attraction. In the liquid state, the molecules have more energy and move about more. 4 They may form brief clusters, but the sample does not have a rigid structure and can flow or settle into...
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