Physical Chemistry , 1st ed.

We can rearrange the equation relating volumes and temperatures above to get

V

V

f

i







T

T

f

i

 (2.46)

It can be shown that equals ^23 for a monatomic ideal gas.* Thus,

V

V

f

i



2/3



T

T

f

i

 (2.47)

for an adiabatic, reversible change of a monatomic ideal gas. If we did this in

terms of pressure instead of volume, we would find that



p

p

f

i



2/5



T

T

f

i

 (2.48)

If equations 2.47 and 2.48 were combined algebraically, one would derive

p 1 V 1 5/3p 2 V 2 5/3 (2.49)

which is a special case of Boyle’s law for ideal gases undergoing reversible, adi-

abatic processes. However, in this case, it is not assumed that the temperature

is held constant.

Example 2.13

For an adiabatic, reversible change in 1 mole of an inert monatomic gas, the

pressure changes from 2.44 atm to 0.338 atm. If the initial temperature is

339 K, what is the final temperature?

Solution

Using equation 2.48,



0

2

.3

.4

3

4

8

a

a

t

t

m

m



2/5



33

T

9

f

K



Solving:

Tf154 K

2.9 Phase Changes

So far, we have considered only physical changes of gaseous systems. We have

not yet considered changes in phase, nor chemical changes. We introduce the

application of the ideas discussed so far to those kinds of processes now, start-

ing with changes in phase.

In most cases, changes in phase (solid liquid, liquid gas, solid gas)

occur under experimental conditions of constant pressure, so that the heat

involved,q, is also equal to H.†For example, for the melting of ice at its

normal melting point of 0°C:

H 2 O (s, 0°C) →H 2 O (,0°C)

a certain amount of heat is required per gram or per mole in order to change

the phase. However, during the phase change, the temperature does not change.

QP QP QP

50 CHAPTER 2 The First Law of Thermodynamics

*Cpand CVhave different values for ideal polyatomic gases, so also has a different value

in those cases. We won’t consider this topic further here.†

Changes in pressure can also cause phase changes. We will consider this in Chapter 6.