Physical Chemistry Third Edition

1.2 Systems and States in Physical Chemistry 19

The volume of the object is equal toL^3 ,so

V(T+dT)L(T)^3

(

1 +αLdT^3

)

L(T)^3

(

1 + 3 αLdT+3(αLdT)^2 +(αLdT)^3

)

(1.2-20)

SincedTis small, the last two terms are insignificant compared with the term that is

proportional todT.

V(T+dT)L(T)^3 (1+ 3 αLdT) (1.2-21)

The volume at temperatureT+dTis given by

V(T+dT)V(T)+

(

∂V

∂T

)

dTV(T)(1+αdT) (1.2-22)

Comparison of Eq. (1.2-22) with Eq. (1.2-21) shows that

α 3 αL (1.2-23)

This relationship holds for objects that are not necessarily shaped like a cube.

EXAMPLE 1.7

The linear coefficient of expansion of borosilicate glass, such as Pyrex
or Kimax
, is equal

to 3. 2 × 10 −^6 K−^1. If a volumetric flask contains 2.000000 L at 20.0◦C, find its volume at

25.0◦C.

Solution

V(25◦C)V(20◦C)(1+ 3 αL(5. 0 ◦C))

(2.000000 L)(1+3(3. 2 × 10 −^6 )(5. 0 ◦C)) 2 .000096 L

Exercise 1.5

Find the volume of the volumetric flask in Example 1.7 at 100.0◦C.

Moderate changes in temperature and pressure produce fairly small changes in the

volume of a liquid, as in the examples just presented. The volumes of most solids

are even more nearly constant. We therefore recommend the following practice:For

ordinary calculations, assume that liquids and solids have fixed volumes. For more

precise calculations, calculate changes in volume proportional to changes in pressure

or temperature as in Examples 1.5 and 1.6.

Exercise 1.6

The compressibility of acetone at 20◦Cis12. 39 × 10 −^10 Pa−^1 , and its density is 0.7899 g cm−^3

at 20◦C and 1.000 bar.

a.Find the molar volume of acetone at 20◦C and a pressure of 1.000 bar.

b.Find the molar volume of acetone at 20◦C and a pressure of 100.0 bar.