the gas inside the container, as shown in Figure 11.6. Moreover, imagine that we immerse the
capsule in a surrounding whose temperature we can lower. Of course, if we allow enough time,
the temperature of the gas inside the container will reach the temperature of its surroundings.
Also keep in mind that because the gas is contained inside a rigid container, it has a constant
volume and a constant mass. Now, what happens to the pressure of the gas inside the container
as indicated by the pressure gauge as we decrease the surrounding temperature? The pressure
will decrease as the temperature of the gas is decreased. We can determine the relationship
between the pressure and the temperature using the ideal gas law, Equation (11.3).
Now, let us proceed to run a series of experiments. Starting with the surrounding temper-
ature equal to some reference temperature — say,Tr— and allowing enough time for the con-
tainer to reach equilibrium with the surroundings, we then record the corresponding pressure
of the gas,Pr. The pressure and temperature of the gas are related according to the ideal gas law:(11.4)
Now imagine that we lower the surrounding temperature toT 1 , once equilibrium is reached,
recording the pressure of the gas and denoting the reading byP 1. Because the temperature of
the gas was lowered, the pressure would be lowered as well.(11.5)
Dividing Equation (11.5) by Equation (11.4), we have
(11.6)
And after canceling out them, theR, and theV, we have
(11.7)
T 1
Tr
P 1
Pr
T 1
Tr
P 1 V
mR
PrV
mR
T 1
P 1 V
mR
Tr
PrV
mR
312 Chapter 11 Temperature and Temperature-Related Parameters
Surrounding
Capsule
■Figure 11.6
The capsule used in the absolute
zero temperature example.Copyright 2010 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s).圀圀圀⸀夀䄀娀䐀䄀一倀刀䔀匀匀⸀䌀伀䴀圀圀圀⸀夀䄀娀䐀䄀一倀刀䔀匀匀⸀䌀伀䴀