Page 45 - Physical chemistry understanding our chemical world

12 INTRODUCTION TO PHYSICAL CHEMISTRY

This last paragraph inevitably leads to the questions, ‘So how do we know what
the exact temperature is?’ and ‘How do I know if my thermometer follows profile
(a) or profile (b) in Figure 1.4?’ Usually, we do not know the answer. If we had a
single thermometer whose temperature was always accurate then we could use it as a
primary standard, and would simply prepare a calibrated thermometer against which
all others are calibrated.
But there are no ideal (perfect) thermometers in the real world. In practice, we
generally experiment a bit until we find a thermometer for which a property X is as
close to being a linear function of temperature as possible, and call it a standard ther-
mometer (or ‘ideal thermometer’). We then calibrate other thermometers in relation to
this, the standard. There are several good approximations to a standard thermometers
available today: the temperature-dependent (observed) variable in a gas thermometer
is the volume of a gas V . Provided the pressure of the gas is quite low (say, one-
hundredth of atmospheric pressure, i.e. 100 Pa) then the volume V and temperature
T do indeed follow a fairly good linear relationship.
A second, popular, standard is the platinum-resistance thermometer. Here, the elec-
trical resistance R of a long wire of platinum increases with increased temperature,
again with an essentially linear relationship.

Worked Example 1.1 A platinum resistance thermometer has a resistance R of 3.0 ×
◦
◦
10 −4 at 0 Cand 9.0 × 10 −4 at 100 C. What is the temperature if the resistance R
is measured and found to be 4.3 × 10 −4 ?
We first work out the exact relationship between resistance R and temperature T .We
must assume a linear relationship between the two to do so.
The change per degree centigrade is obtained as ‘net change in
These discussions are resistance ÷ net change in temperature’. The resistance R increases
−4
◦
expressed in terms of by 6.0 × 10 while the temperature is increased over the 100 C
centigrade, although range; therefore, the increase in resistance per degree centigrade is
absolute temperatures given by the expression
are often employed –
see next section. ◦ 6.0 × 10 −4 −6 ◦ −1
R per C = = 6 × 10 C
100 C
◦
Next, we determine by how much the resistance has increased in going to the new
(as yet unknown) temperature. We see how the resistance increases by an amount (4.3 −
3.0) × 10 −4 = 1.3 × 10 −4 .
The increase in temperature is then the rise in resistance divided by the change in
resistance increase per degree centigrade.
We obtain
1.3 × 10 −4
◦
6 × 10 −6 C −1
◦
so the new temperature is 21.7 C.