The extent to which one form of energy can be converted into another is limited by practical considerations. The fraction converted in a given process is often re­ferred to as the efficiency of the process. Thus, in converting x units of energy in form A to y units in form B, the percentage efficiency is defined as 100y/x. The energy not converted to form B (i. e., x — y units) may remain in form A or may find its way into other forms (C, D, etc.) as a result of the process.

An example of energy conversion leading to power generation is hydroelec­tric power generation. The potential energy of the water in a mountain reservoir or lake is first converted into kinetic energy of a turbine, which in turn is converted into electrical energy by means of a generator. All of these energy conversion processes are quite efficient; with good design they might even approach 100% efficiency. The energy not converted to electrical energy in this process is mainly dissipated by increasing the thermal energy of the water leaving the power station.

Another common example of energy conversion is that of converting the chemical of fossil fuels (e. g., coal or oil) into electrical ^energy through the

medium of a conventional power station. "Tils case is ilustrated in Figure 1.2. Suppose that we start with 1W GJ* of chemical energy in the form of coal. ^uls energy is released at a high temperature (typically 2000°C). Some of the energy (typically 10 GJ) leaves the power station as thermal energy in the flue gases going up the stack. However, most is transferred by thermal radiation and con-

•One gigajoule of energy would be sufcient to power a 1 00-watt light bulb for 116 days (nearly 4 months).

Fi^are 1.2: Energy conversion in a power station.

vection to the water in the boiler tubes, converting this water into high-pressure steam at perhaps 500°C. This steam is passed into a turbine, where some of the thermal energy is converted into electrical energy (typically 35 GJ), and the rest of the original energy (55 GJ) is rejected as thermal energy into lukewarm cool­ing water at 25-40°C.

Thus, only about one-third of the original chemical energy in the coal has ac­tually been converted into a useful alternative form, namely, electrical energy. The efficiency achievable in the conversion of thermal energy (the intermediate form of energy in the process described here) into electrical energy is deter­mined by the temperature range over which the process operates. If we were able to reject the heat at a temperature close to absolute zero, the residual ther­mal energy would be negligible. However, we are forced to reject the energy at a temperature slightly above that of our normal surroundings, at which temper­ature a very large amount of the thermal energy still remains. Thus, if we lived on a planet where the ambient conditions were close to absolute zero, our en­ergy conversion efficiencies could be made much higher, though there would be some other difficulties. This basic limitation on the conversion of thermal en­ergy into other useful forms is fundamental to thermodynamics.

We may make better use of the chemical energy used in power generation if we can use the thermal energy leaving the station directly, for example, for domestic or industrial heating. However, this heat is not very useful at the luke­warm temperatures of the cooling water. A combined heat and power (CHP) station rejects heat at a higher and more useful temperature (100°C, say), but, for the reasons explained above, this leads to some reduction in the electrical output of the station. This trade-off between heat and power generation can sometimes be economic, particularly where there is a large demand for heat. Thus, CHP stations have found extensive application for power generation and district heating in the Scandinavian countries and Russia.

A device for converting thermal energy into another form of energy (kinetic, potential, electrical, etc.) is referred to as a heat engine. A typical heat engine would be the turbine of a power station. Other examples are the jet engine of an airplane and the internal combustion engine of an automobile. All these de­vices take thermal energy generated at a temperature 7j, carry out some form of energy conversion, and reject the residual thermal energy at a lower tempera­ture, TY Here, Tv and ‘Fz designate temperatures on the absolute (kelvin) scale of temperature. The maximum efficiency 11 obtainable from any heat engine is given by an equation first derived by Carnot in 1824:

This equation shows that if r; is zero on the absolute scale, the efficiency can theoretically approach unity (i. e., 100%). However, in practice it is necessary to reject the heat at a temperature somewhat above normal ambient temperature (e. g., 300 K or 27°C). Thus, the maximum efficiency is likely to be around 50—60% in a common heat engine, with practical efficiencies being lower than this because of departures from ideal behavior.