156 ATOMS, IONS, SALTS, AND SURFACES 



steel show that it is necessary to apply a force of 100,000 lb. to rupture a bar i sq.in. in 

 cross-section. If it were possible to carry out a tensile-strength test in an ideal way 

 such that the bar (of i sq.cm. cross-section; see Fig. 12) would not be deformed before 

 the break occurs, and so that the rupture would give two plane surfaces at right angles 

 to the longitudinal axis of the bar, then the energy used would be equal to twice the 

 free surface energy (27) per square centimeter at the temperature of the test. This is 

 true because all that occurs in such an ideal rupture is the formation of a new surface on 

 the steel of 2-sq.cm. area. This is equal numerically to twice the surface tension of 

 steel per centimeter. The work necessary thus to pull apart a bar of unit cross-section 

 may be designated as the work of cohesion {Wc). 



Wc = 2y. (i) 



If an endeavor is made to apply such a tensile-strength test to a bar of liquid, it is 

 found that certain experimental difficulties arise. Nevertheless, the numerical value 

 of the work of cohesion is known with considerable accuracy in such a case, since it 

 may be obtained from the surface tension of the liquid. 



The surface tension of water at 20° is 72.8 dynes per centimeter, so its work of co- 

 hesion is 145.6 ergs per square centimeter. This small value may seem to indicate a 

 small tensile strength (force of cohesion) in water, but just the opposite is true since 

 the distance to which molecular attraction remains appreciable is very small, and is 

 only of the order of molecular dimensions. Furthermore, it decreases as a moderately 

 high power of the distance. Suppose that the summation of this rapidly decreasing 

 force is equivalent to the action of a constant force through io~^ cm. Then the force 

 of cohesion would be 



■ _ or 1 .4s6X 10'° dynes = 1 .48X lo^ gm. per square centimeter , 

 10 * 



or about 14,000 atm. The theory of van der Waals indicates a value of about 11,000 

 atm., while other methods of calculation usually give between 10,000 and 15,000. 



LATENT HEAT OF A SURFACE 



According to the rule of Le Chatelier, if the state of a system is changed, the sys- 

 tem alters in such a way as to oppose a resistance to that change. Thus if the solubil- 

 ity of a salt increases with the temperature, the last amount of salt which dissolves to 

 saturate the solution produces a cooling, since this cooling lowers the solubility, and 

 thus opposes the solution of the salt. Now, since the surface tension decreases with rise 

 of temperature (Fig. 8), a surface must cool if it is expanded, since by cooling the surface 

 tension is increased, and this opposes an extra resistance to the further extension. 



That heat should be used up in the formation of a surface is to be expected on 

 other grounds. In the vaporization of a liquid the kinetic energy of molecular vibra- 

 tion of the molecules of the liquid, which determines the temperature, is partly con- 

 verted into molecular potential energy, i.e., the molecular energy of motion is utilized 

 in the separation of each molecule from its neighbors and against the attraction which 

 they exert. Now since a molecule which is in the interior of a liquid must move into 



