Page 72 - Physical chemistry eng

3.1 THE MATHEMATICAL PROPERTIES OF STATE FUNCTIONS 49

TABLE 3.2 Isothermal Compressibility at 298 K
6
6
Substance 10 k>bar -1 Substance 10 k>bar -1
Al(s) 1.33 Br 2 (l) 64
SiO 2 (s) 2.57 C 2 H 5 OH(l) 110
Ni(s) 0.513 C 6 H 5 OH(l) 61

TiO 2 (s) 0.56 C 6 H 6 (l) 94
Na(s) 13.4 CCl 4 (l) 103
Cu(s) 0.702 CH 3 COCH 3 (l) 125
C(graphite) 0.156 CH 3 OH(l) 120

Mn(s) 0.716 CS 2 (l) 92.7
Co(s) 0.525 H 2 O(l) 45.9
Au(s) 0.563 Hg(l) 3.91
Pb(s) 2.37 SiCl 4 (l) 165

Fe(s) 0.56 TiCl 4 (l) 89
Ge(s) 1.38
Sources: Benenson, W., Harris, J. W., Stocker, H., and Lutz, H. Handbook of Physics. New York: Springer,
2002; Lide, D. R., ed. Handbook of Chemistry and Physics. 83rd ed. Boca Raton FL: CRC Press, 2002;
Blachnik, R., ed. D’Ans Lax Taschenbuch für Chemiker und Physiker. 4th ed. Berlin: Springer, 1998.

The second expression in Equation (3.11) holds if ¢T and ¢V are small enough that b
and are constant over the range of integration. Example Problem 3.2 shows a useful
k
application of this equation.

EXAMPLE PROBLEM 3.2
You have accidentally arrived at the end of the range of an ethanol-in-glass ther-
mometer so that the entire volume of the glass capillary is filled. By how much will
the pressure in the capillary increase if the temperature is increased by another
-5
10.0°C? b glass = 2.00 * 10 (°C) -1 , b ethanol = 11.2 * 10 -4 (°C) -1 , and
-5
k ethanol = 11.0 * 10 (bar) -1 . Will the thermometer survive your experiment?
Solution
Using Equation (3.11),
b 1 b 1 V f
¢P = ethanol dT - dV L ethanol ¢T - ln
k kV k k V
L L i
i glass
i
= b ethanol ¢T - 1 ln V (1 + b glass ¢T) L b ethanol ¢T - 1 V b ¢T
k k V i k k V i
(b ethanol - b glass )
= ¢T
k
(11.2 - 0.200) * 10 -4 (°C) -1
= * 10.0°C = 100. bar
-5
11.0 * 10 (bar) -1
In this calculation, we have used the relations V(T ) = V(T )(1 + b[T - T ]) and
2
1
2
1
ln(1 + x) L x if x V 1 .
The glass is unlikely to withstand such a large increase in pressure.