Mechanical Equivalent Of Heat

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Mechanical Equivalent of Heat

[Abstract / Introduction]

Long before physicists recognized that heat is a form of energy transfer resulting from the random microscopic motion of atoms, they defined heat in terms of the temperature changes it produces in a body. The traditional unit of heat is the calorie (cal), which is the amount of heat needed to raise the temperature of 1 g of water by 1¢ªC. The kilocalorie is 1000 cal: 1 kcal = 1000 cal. Incidentally, the calories marked on some packages of food in grocery stores are actually kilocalories, sometimes called large calories.
The heat necessary to raise the temperature of 1 kg of a material by 1¢ªC is called the specific heat capacity, or the specific heat, usually designated by the symbol c. Thus, by definition, water has a specific heat of: c = 1 kcal/kg·¢ªC. Specific heat varies from substance to substance (see Appendix A, Table A4), and varies with temperature. For example, the specific heat of water varies by about 1% between 0¢ªC and 100¢ªC, reaching a minimum of 35¢ªC. This variation must be taken into account for a precise definition of the calorie: a calorie is the heat needed to raise the temperature of 1 g of water from say, 14.5¢ªC to 15.5¢ªC. Finally, the specific heat depends on the pressure to which the material is subjected during the heating.
Since specific heat is defined as the amount of heat required to increase the temperature of 1kg of a given substance by 1¢ªC, the amount of heat Q required to increase the temperature of a mass m by ¥ÄT is proportional to m and to ¥ÄT and can be found by the equation: Q = m c ¥ÄT. This merely says that a large mass or a large temperature change requires more heat, in proportion to the mass and to the temperature change. Incidentally, work is defined as a force applied through a distance. For rotational motion, work is equal to the torque applied through an angular displacement, ...