THERMODYNAMIC PROPERTIES OF SUBSTANCES. 53 



initial state a straight line be drawn in the plane perpendicular to 

 the axis of v, so that the tangent of the angle which it makes with 

 the direction of the axis of r\ shall be equal to the given temperature 

 if, it may easily be shown that the vertical projections of the two 

 segments of this line made by the point of the initial state and the 

 surface of dissipated energy represent the two quantities required.* 



These problems may be modified so as to make them approach 

 more nearly the economical problems which actually present them- 

 selves, if we suppose the body to be surrounded by a medium of 

 constant pressure and temperature, and let the body and the medium 

 together take the place of the body in the preceding problems. The 

 results would be as follows : 



If we suppose a plane representing the constant pressure and tem- 

 perature of the medium to be tangent to the surface of dissipated 

 energy of the body, the distance of the point representing the initial 

 state of the body from this plane measured parallel to the axis, of e 

 will represent the available energy of the body and medium, the 

 distance of the point to the plane measured parallel to the axis of ij 

 will represent the capacity for entropy of the body and medium, the 

 distance of the point to the plane measured parallel to the axis of v 

 will represent the magnitude of the greatest vacuum which can be 

 produced in the body or medium (all the power used being derived 

 from the body and medium); if a line be drawn through the point 

 in a plane perpendicular to the axis of v, the vertical projection of the 

 segment of this line made by the point and the tangent plane will 

 represent the greatest amount of heat which can be given to or taken 

 from another body at a constant temperature equal to the tangent of 

 the inclination of the line to the horizon. (It represents the greatest 

 amount which can be given to the body of constant temperature, if 

 this temperature is greater than that of the medium ; in the reverse 

 case, it represents the greatest amount which can be withdrawn from 

 that body.) In all these cases, the point of contact between the plane 

 and the surface of dissipated energy represents the final state of the 

 given body. 



If a plane representing the pressure and temperature of the medium 

 be drawn through the point representing any given initial state of 

 the body, the part of this plane which falls within the surface of 

 dissipated energy will represent in respect to volume, entropy, and 

 energy all the states into which the body can be brought by rever- 

 sible processes, without producing permanent changes in external 

 bodies (except in the medium), and the solid figure included between 



*Thus, in figure 3, if the straight line MAN be drawn so that tan NAC = *', MR 

 will be the greatest amount of heat which can be given to the body of constant 

 temperature and NS will be the greatest amount which can be taken from it. 



