93 Measuring Body Temperature

Liquid Thermometers

We now know that an increase in corresponds to an increase in the average of atoms and molecules. A result of that increased motion is that the average distance between atoms and molecules increases as the temperature increases. This phenomenon, known as is the basis for temperature measurement by liquid .

A glass tube filled with a colored liquid and marked with evenly spaced divisions and temperature values.
A clinical thermometer based on the thermal expansion of a confined liquid. Image Credit: Clinical Thermometer by Menchi via Wikimedia Commons

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Common liquid thermometers use the of alcohol confined within a glass or plastic tube to measure . Due to thermal expansion, the alcohol volume changes with temperature. The thermometer must be by marking the various fluid levels when the thermometer is placed in an environment with a known temperature, such as water boiling at sea level.

Reinforcement Exercise

You may have noticed that when you place a liquid thermometer into hot water, the liquid level actually drops momentarily, before beginning to climb as expected. Knowing what you do about , can you explain why this occurs?

Bimetallic Strips

Different materials will thermally expand (or contract) by different amounts when heated (or cooled). Bimetallic strips rely on this phenomenon to measure . When two different materials are stuck together, the resulting structure will bend as the temperature changes due to the different experienced by each material.

Figure a shows two vertical strips attached to each other. It is labeled T0. Figure b shows the same two strips bent towards the right, but still attached so the strip on the outside of the bend is longer. It is labeled T greater than T0.
The curvature of a bimetallic strip depends on temperature. (a) The strip is straight at the starting temperature, where its two components have the same length. (b) At a higher temperature, this strip bends to the right, because the metal on the left has expanded more than the metal on the right. At a lower temperature, the strip would bend to the left. Image Credit: Openstax University Physics

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Linear Thermal Expansion

For most common materials the change in length (Delta L) caused by a change in temperature (Delta T) is proportional to the original length (L_0) and can be modeled using the (\alpha) and the following equation:

(1)   \begin{equation*} \Delta L = \alpha L_0 \Delta T \end{equation*}

The following table provides the linear thermal expansion coefficients for different solid materials. More expansive (ha!) tables can be found online.

Thermal Expansion Coefficients
Material Coefficient of Linear Expansion (1/°C)
Solids
Aluminum 25 × 10−6
Brass 19 × 10−6
Copper 17 × 10−6
Gold 14 × 10−6
Iron or steel 12 × 10−6
Invar (nickel-iron alloy) 0.9 × 10−6
Lead 29 × 10−6
Silver 18 × 10−6
Glass (ordinary) 9 × 10−6
Glass (Pyrex®) 3 × 10−6
Quartz 0.4 × 10−6
Concrete, brick ~12 × 10−6
Marble (average) 2.5 × 10−6

Everyday Example

The main span of San Francisco’s Golden Gate Bridge is 1275 m long at its coldest. The bridge is exposed to temperatures ranging from –15 °C to 40 °C. What is its change in length between these temperatures? Assume that the bridge is made entirely of steel.

We can use the equation for linear :

    \begin{equation*} \Delta L = \alpha L_0 \Delta T \end{equation*}

Substitute all of the known values into the equation, including the for steel and the initial and final temperatures:

    \begin{equation*} \Delta L = 12 \times 10^{-6} \frac{1}{\bold{^{C\circ}}}(1275\,\bold{m})\left( 40\,\bold{^{\circ}C}-(15\,\bold{^{\circ}C})\right) = 0.84\,\bold{m} \end{equation*}

Although not large compared to the length of the bridge, the change in length of nearly one meter is observable and important. Thermal expansion could causes bridges to buckle if not for the incorporation of gaps, known as expansion joints, into the design.

Two slabs of concrete on a bridge surface are separated by a gap covered with a metal plate that is free to slide.
Expansion joint on the Golden Gate Bridge. Image Credit: Expansion Joint Golden Gate Bridge by Michiel1972 via Wikimedia Commons

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Reinforcement Exercises

A deep-space satellite made primarily of aluminum is 12 m long when launched at 22 °C (72 °F).

If the satellite comes eventually come to with the cosmic microwave background temperature at -270.45 °C  (-455 °F).[4]

How much will the satellite change length?

What will the new length be?

Temperature Units

 measure according to well-defined scales of measurement. The three most common temperature scales are , , and . On the Celsius scale, the freezing point of water is °C and the boiling point is 100 °C. The unit of temperature on this scale is the degree Celsius (°C). The Fahrenheit scale (°F) has the freezing point of water at 32 °F and the boiling point 212 °F.  You can see that 100 Celsius degrees span the same range as 180 Fahrenheit degrees. Thus, a temperature difference of one degree on the Celsius scale is 1.8 times as large as a difference of one degree on the Fahrenheit scale, as illustrated by the top two scales in the following diagram.

Figure shows Farhenheit, Celsius and Kelvin scales. In that order, the scales have these values: absolute zero is minus 459, minus 273.15 and 0, freezing point of water is 32, 0 and 273.15, normal body temperature is 98.6, 37 and 310.15, boiling point of water is 212, 100 and 373.15. Zero degree F is minus 17.8 degree C and 255.25 degree K. The relative sizes of the scales are shown on the right. A difference of 9 degrees F is equivalent to 5 degrees C and 5 degrees K.
Relationships between the Fahrenheit, Celsius, and Kelvin temperature scales are shown. The relative sizes of the scales are also shown. Image Credit: Temperature Scales diagram from OpenStax University Physics[/footnote]

The Kelvin Scale

The definition of in terms of molecular motion suggests that there should be a lowest possible temperature, where the average microscopic of molecules is zero (or the minimum allowed by the quantum nature of the particles). Experiments confirm the existence of such a temperature, called . An absolute temperature scale is one whose zero point corresponds to . Such scales are convenient in science because several physical quantities, such as the pressure in a gas, are directly related to absolute temperature. Additionally,  absolute scales allow us to use ratios of temperature, which relative scales do not. For example, 200 K is twice the of 100 K, but 200 °C is not twice the temperature of 100 °C.

The Kelvin scale is the absolute temperature scale that is commonly used in science. The temperature unit is the , which is abbreviated K (but not accompanied by a degree sign). Thus 0 K is absolute zero, which corresponds to -273.15 °C. The size of Celsius and Kelvin units are set to be the same so that differences in temperature (\Delta T) have the same value in both Kelvins and degrees Celsius. As a result, the freezing and boiling points of water in the Kelvin scale are 273.15 K and 373.15 K, respectively, as illustrated in the previous diagram.

You can convert between the various temperature scales using equations or various conversation programs, including some accessible online.

Reinforcement Exercise

Convert 50 °F to °C and then to K.

Temperature Measurement

In addition to , other temperature dependent physical properties can be used to measure temperature. Such properties include electrical resistance and optical properties such as reflection, emission and absorption of various colors.  Light-based temperature measurement will come up again in the next chapter.

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