Physical Chemistry Third Edition

2.5 Enthalpy 77

P 2

P 1



(

V 1

V 2

)γ

(2.5-16b)

T 2

T 1



(

P 2

P 1

) 1 − 1 /γ

(2.5-16c)

Exercise 2.23

Verify Eq. (2.5-16).

For many solids in which a single atom is the formula unit, the molar heat capacity

at room temperature is approximately equal to 3R 24 .94 J K−^1 mol−^1. This is the

law of Dulong and Petit, which is a good approximation near room temperature and

becomes more nearly accurate at higher temperatures.

Pierre Louis Dulong, 1785–1838, was a
French chemist originally trained as a
physician. Alexis Thérèse Petit,
1791–1820, was a French physicist.
EXAMPLE2.22
Find the percent differences betweenCP, mof solid silver and 3Rat 298.15 K.
Solution
From the appendix,CP, m= 25.351 J K−^1 mol−^1

percent difference

25 .351JK−^1 mol−^1 − 24 .944JK−^1 mol−^1

24 .944JK−^1 mol−^1

×100%− 1 .6%

Exercise 2.24

Repeat the calculation of the previous example for iron.

The Joule–Thomson Experiment

For an ideal gasUdepends only onTandn, so thatHdepends only onTandn:

HU+PVU(T,n)+nRTH(T,n) (ideal gas) (2.5-17)

Therefore,

(

∂H

∂P

)

T,n

0 (ideal gas) (2.5-18)

Joule and Thomson carried out experiments in the 1850s to determine the value of

(∂H/∂P)T,nfor real gases. They used an apparatus equivalent to that sketched in

Figure 2.8. This apparatus consists of two cylinders fitted with pistons and a porous