Concise Physical Chemistry

c11 JWBS043-Rogers September 13, 2010 11:26 Printer Name: Yet to Come

168 LIQUIDS AND SOLIDS

making it a simple matter to measure the surface tension of a liquid of densityρthat

rises to a heighthin a capillary of known radiusRagainst the acceleration due to

gravity,g= 9 .807 m s−^2.

11.2 HEAT CAPACITY OF LIQUIDS AND SOLIDS

In 1907 Einstein showed that the heat capacity of many solids is 25 J K−^1 mol−^1

(in agreement with the prior law of Dulong and Petit) but that at some characteristic

temperature it drops off along a sigmoidal curve to zero at 0 K (Fig. 11.5). Although

his derivation is general, he used it to describe the heat capacity of diamond, an

exceptional solid because of its strong tetrahedral bonding. The resulting curve, one

of the most famous of twentieth-century science, was based on the new quantum

theory of Max Planck, which might otherwise have gone unnoticed by many in the

physics community. The success of Einstein’s theory of heat capacities is shown in a

reproduction of his original graph depicting the theoretical heat capacity of diamond

(solid curve) compared to known experimental points.

In general, the molar heat capacity of a liquid is higher than the molar heat capacity

of a gas because molecular motion in the liquid state implies distortion of the liquid

structure in the vicinity of the moving molecule. This is what we would expect if

we think of a liquid as an extremely nonideal gas. An example is mercury, which

has the heat capacity of an ideal gas,^32 R∼= 12 .5JK−^1 mol−^1 in the vapor state, but

hasCV= 23 .6JK−^1 mol−^1 in the liquid state. Notice how close liquid mercury is

T, K

0 200 400 600 800 1000 1200 1400 1600

C

, cal KE

-1

mol

-1

0

1

2

3

4

5

6

FIGURE 11.5 Heat capacity as a function of temperature. Einstein calculated the theoretical

curve of the heat capacity of diamond (solid line) and compared it to known experimental

points. Heat was normally measured in calories in Einstein’s time. For more detail, see Rogers

(2005).