Measurement and Control Basics Fourth Edition

Chapter 7 - Temperature Measurement: Bimetallic Thermometers

A bimetallic strip curves or twists when exposed to a temperature change,
as Figure 7-2 shows, because of the different thermal expansion coefficients
of the metals used in it. Bimetallic temperature sensors are based on
the principle that different metals experience thermal expansion with
changes in temperature. To understand thermal expansion, consider a
simple model of a solid, the atoms of which are held together in a regular
array of forces that have an electrical origin. The forces between atoms can
be compared to the forces that would be exerted by an array of springs
connecting the atoms together. At any temperature above absolute zero
(-273.15°C), the atoms of the solid vibrate. When the temperature is
increased, the amplitude of the vibrations increases, and the average distance
between atoms increases. This leads to an expansion of the whole
body as the temperature is increased. The change in length that arises
from a change in temperature (?T) is designated by ?L. Through
experimentation, we find that the change in length ?L is proportional to the
change in temperature ?T and the original length L. Thus,

?L= kL?T

(7-7)

EXAMPLE 7-3

Problem: A gas in a fixed volume has a pressure of 30 psi at a temperature of
20°C. What is the temperature in °C if the pressure in the detector has
increased to 35 psi?

Solution: First, convert the temperature of 20°C to the absolute scale of
Kelvin using Equation 7-1:

Now, use Equation 7-6 to find the new temperature that the detector is
measuring:

Finally, convert this value for T₂ to °C:

Figure 7-2. Bimetallic strip

where k is called the coefficient of linear expansion. This coefficient has different
values for different materials. Table 7-2 lists the experimentally
determined values for the average coefficient of linear expansion of several
common solids in the temperature range of 0 to 100°C.

Table 7-2. Thermal Expansion Coefficient

Example 7-4 illustrates how to calculate the expansion of a metal rod with
a temperature increase.

EXAMPLE 7-4

Problem: How much will a 4 m-long copper rod expand when the
temperature is changed from 0 to 100°C?

Solution: First, find the length of the rod at 0°C and at 100°C, then find the
change in length. Using Equation 7-7 at 0°C,

At 100°C we have the following:

Thus, the expansion in the rod is L₁₀₀- L_o = 0.00661 m

Figure 7-3 shows a typical bimetallic dial thermometer using a spiral
wound element. The spiral element provides a larger bimetallic element in
a smaller area, and it can measure smaller changes in temperature. It is a
low-cost instrument but has the disadvantages of relative inaccuracy and
a relatively slow response time. It is normally used in temperature measurement
applications that do not require high accuracy.

Figure 7-3. Bimetallic dial thermometer

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Chapter 7 - Temperature Measurement: Bimetallic Thermometers

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