79 Measuring Body Temperature

Homeostatis

In the previous unit we learned that the body is not very efficient at converting chemical potential energy to useful work. The majority of chemical potential energy becomes thermal energy. We also learned that even when not attempting to do useful work, the basic metabolic processes of the body will convert significant chemical energy to thermal energy. So far in this very unit we have learned that inelastic collisions and friction within the body will each convert kinetic energy to thermal energy.  The total rate at which other types of energy are converted to thermal energy is known as the thermal power. The body typically exhausts this thermal energy to the environment in order to maintain constant  body temperature. However, if the exhaust power does not match the thermal power, then body temperature will change and thermal injury can occur. If the exhaust power is too low then thermal energy builds up and body temperature rises, leading to hyperthermia. Conversely, if the exhaust power is too high then body temperature drops, leading to hypothermia.

A diagram shows the temperatures in Fahrenheit at which various states of hypothermia and hyperthermia occur, relative to body temperature. From high to low temperature: Death at 108 and above, Hyperplexia (medical emergency) at 106.7, Fever (medical significance) 101.5, Normal 98.6, Hypothermia, 95, Severe Hypothermia, 82.4, Uncounsciousness 82, Death 77 and below.
False-color scale indicating medically-relevant body temperature thresholds. Image Credit:Human Body Temperature Scale by Foxtrot620 via Wikimedia Commons

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MEasuring body Temperature

In order to analyze how our body exhausts thermal energy and maintains a constant temperature we need to carefully define temperature and discuss how it can be measured. Temperature  (T) is a measure of the average thermal energy per atom or molecule. We already know that thermal energy is just kinetic energy stored in the microscopic motion of atoms and molecules so we can also think of temperature as a measure of the average kinetic energy per atom or molecule. Therefore, with increasing temperature comes an increase in atomic motion and a requirement for greater space between atoms to accommodate that motion. This phenomenon, known as thermal expansion is the basis for temperature measurement by liquid thermometer.

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 thermal expansion of alcohol confined within a glass or plastic tube to measure temperature. Due to thermal expansion, the alcohol volume changes with temperature. The thermometer must be calibrated 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

Reinforcement Exercises

Bimetallic Strips

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

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

Substitute all of the known values into the equation, including the linear thermal expansion coefficient 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

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Temperature Units

Thermometers measure temperature according to well-defined scales of measurement. The three most common temperature scales are Fahrenheit, Celsius, and Kelvin. On the Celsius scale, the freezing point of water is 0 °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 temperature in terms of molecular motion suggests that there should be a lowest possible temperature, where the average microscopic kinetic energy of molecules is zero (or the minimum allowed by the quantum nature of the particles). Experiments confirm the existence of such a temperature, called absolute zero. An absolute temperature scale is one whose zero point corresponds to absolute zero. 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 temperature 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 SI temperature unit is the Kelvin, 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

Temperature Measurement

In addition to thermal expansion, 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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  1. Human Body Temperature Scale by Foxtrot620 [CC BY-SA 4.0 (https://creativecommons.org/licenses/by-sa/4.0)], from Wikimedia Commons ↵
  2. Clinical Thermometer by Menchi [GFDL (http://www.gnu.org/copyleft/fdl.html) or CC-BY-SA-3.0 (http://creativecommons.org/licenses/by-sa/3.0/)] via Wikimedia Commons ↵
  3. OpenStax University Physics, University Physics. OpenStax CNX. May 10, 2018 http://cnx.org/contents/74fd2873-157d-4392-bf01-2fccab830f2c@5.301. ↵
  4. Michiel1972 [CC BY-SA 3.0 (https://creativecommons.org/licenses/by-sa/3.0)], via Wikimedia Commons ↵
  5. "Web-based hypothermia information: a critical assessment of Internet resources and a comparison to peer-reviewed literature" by Dr. Eric Christian, Cosmicopia, NASA is in the Public Domain ↵
  6. Significant content in this chapter was adapted from OpenStax University Phyiscs which you can download for free at http://cnx.org/contents/a591fa18-c3f4-4b3c-ad3e-840c0a6e95f4@1.322. ↵
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