Simple Nature - Light and Matter

a / 1. The temperature differencebetween the hot and cold parts ofthe air can be used to extract mechanicalenergy, for example witha fan blade that spins becauseof the rising hot air currents. 2.If the temperature of the air isfirst allowed to become uniform,then no mechanical energy canbe extracted. The same amountof heat energy is present, but itis no longer accessible for doingmechanical work.b / A heat engine. Hot airfrom the candles rises throughthe fan blades, and makes theangels spin.c / Sadi Carnot (1796-1832)5.3.2 Heat enginesHeat may be more useful in some forms than in others, i.e., thereare different grades of heat energy. In figure a/1, the difference intemperature can be used to extract mechanical work with a fanblade. This principle is used in power plants, where steam is heatedby burning oil or by nuclear reactions, and then allowed to expandthrough a turbine which has cooler steam on the other side. On asmaller scale, there is a Christmas toy, b, that consists of a smallpropeller spun by the hot air rising from a set of candles, very muchlike the setup shown in figure a.In figure a/2, however, no mechanical work can be extractedbecause there is no difference in temperature. Although the air ina/2 has the same total amount of energy as the air in a/1, the heatin a/2 is a lower grade of energy, since none of it is accessible fordoing mechanical work.In general, we define a heat engine as any device that takes heatfrom a reservoir of hot matter, extracts some of the heat energy to domechanical work, and expels a lesser amount of heat into a reservoirof cold matter. The efficiency of a heat engine equals the amount ofuseful work extracted, W , divided by the amount of energy we hadto pay for in order to heat the hot reservoir. This latter amountof heat is the same as the amount of heat the engine extracts fromthe high-temperature reservoir, Q H . (The letter Q is the standardnotation for a transfer of heat.) By conservation of energy, we haveQ H = W + Q L , where Q L is the amount of heat expelled into thelow-temperature reservoir, so the efficiency of a heat engine, W/Q H ,can be rewritten asefficiency = 1 − Q LQ H. [efficiency of any heat engine]It turns out that there is a particular type of heat engine, theCarnot engine, which, although not 100% efficient, is more efficient310 Chapter 5 Thermodynamics