Fig. 29.
The diagram represents the pressure and the volume of a gas when these things change. There are two conditions, (1) when the heat developed by the compression is allowed to escape through the walls of the vessel to the outside, or when the heat lost in the expansion of the gas is compensated by the conduction of heat through the walls of the vessel from outside; and (2) when the heat developed is retained in the gas, as when the latter is contained in a vessel the walls of which do not conduct heat. The pressure of the gas is measured along the horizontal axis, and the volume is measured along the vertical axis, and a curve is drawn so that for any value of the pressure there is a corresponding value of the volume. Thus the values of the pressures p and p1 in the diagram correspond to the value of the volume v. The curve relating the change of pressure with a corresponding change of volume is, in general, that called a rectangular hyperbola. But there are two kinds of such curves: (1) that which we obtain by plotting the corresponding values of pressure and volume, when the temperature of the gas remains constant throughout the series of changes, that is, when the rise of temperature which would occur when the gas is compressed is compensated by the conduction of this heat to the outside of the vessel containing the gas. Such a series of changes of pressure and volume is called an isothermal one. (2) When the heat developed by the compression of the gas is retained in the gas, as when the walls of the vessel in which these changes are effected are such as do not conduct heat: such a series of changes is called an adiabatic one. Adiabatic curves are steeper than are isothermal ones.
THE CARNOT ENGINE
This is an imaginary mechanism which performs a certain cycle of operations. It does not really exist, but the conception of its operation is of the greatest value in the consideration of energy-transformations, and it is for this reason that we discuss it here.
Fig. 30.
Consider a gas, or some other substance capable of expanding or contracting. It contains intrinsic energy, and it is capable of doing work. Thus, since a gas can expand indefinitely it can be made to do mechanical work. A mass of gas at a pressure p1, and having a volume v1, and at a temperature T°, can do work by expanding till its pressure is reduced to p, and its volume increased to v. If it expands adiabatically its temperature will fall to t°. Let us suppose that t° is the temperature of the surrounding medium: the gas cannot therefore cool further, and we can obtain no more work from it. If the gas is the substance which we wish to employ as the working substance in the Carnot engine, we must therefore bring it back to the condition represented by A. That is, we must raise its temperature to T°, we must reduce its volume to v1, and we must increase its pressure to p1.
Thus the steam of an engine is (say) at a temperature of 110° C., and a pressure of 120 lbs. to the square inch. When it has passed through the cylinder and condenser it is water at a temperature of, say, 15° C., and it is at atmospheric pressure. We must, therefore, bring it back to its former condition by heating this water in the boiler till it is steam under the former conditions of temperature and pressure.
Therefore we must, in order to obtain a self-acting engine, cause the working substance, and the mechanism of the engine, to perform a series of cyclical operations.
