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 _p_↓{1} 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. 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 _p_↓{1}, and having a volume _v_↓{1}, 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 _v_↓{1}, and we must increase its pressure to _p_↓{1}. [Illustration: FIG. 30.]