Page 41 - Physical chemistry understanding our chemical world

8 INTRODUCTION TO PHYSICAL CHEMISTRY

Aside

We need to explain the bizarre name of this law, which is really an accident of history.
Soon after the first law of thermodynamics was postulated in the mid nineteenth century,
it was realized how the law presupposed a more elementary law, which we now call
the zeroth law (see below). We call it the ‘zeroth’ because zero comes before one. But
scientists soon realized how even the zeroth law was too advanced, since it presupposed a
yet more elementary law, which explains why the minus-oneth law had to be formulated.

How does a thermometer work?

Thermal equilibrium and the zeroth law of thermodynamics

A fever is often the first visible sign of someone developing an
The word ‘thermometer’
has two roots: meter illness. The body’s temperature rises – sometimes dramatically –
◦
denotes a device to above its preferred value of 37 C. As a good generalization, the
measure something, temperature is hotter when the fever is worse, so it is wise to
and thermo means monitor the temperature of the sick person and thereby check the
‘energy’ or ‘temper- progress of the illness. A thermometer is the ideal instrument for
ature’. Thus, a ‘ther- this purpose.
mometer’ is a device for When measuring a temperature with a thermometer, we place
measuring energy as the mercury-containing end into the patient’s mouth or armpit and
a function of tempera- allow the reading to settle. The mercury is encased within a thin-
ture.
walled glass tube, which itself is placed in contact with the patient.
A ‘reading’ is possible because the mercury expands with increas-
ing temperature: we take the length l of the mercury in the tube to be an accurate
function of its temperature T . We read the patient’s temperature from the thermometer
scale only when the length of the mercury has stopped changing.
But how does the thermometer work in a thermodynamic sense, since at no time
can the toxic mercury be allowed to touch the patient?
Consider the flow of heat: heat energy first flows from the patient
Bodies together at the to the glass, and thence flows through the glass into the mercury.
same temperature are Only when all three – mercury, glass and patient – are at the same
said to be in ‘thermal temperature can the thermometer reading become steady. We say
equilibrium’. we have thermal equilibrium when these three have the same tem-
perature; see Figure 1.3.
Although in some respects a trivial example, a thermometer helps us see a profound
truth: only when both (i) the mercury and the glass, and (ii) the glass and the patient
are at thermal equilibrium can the patient and the mercury truly be said to be at the
same temperature. By this means, we have measured the temperature of the patient by