## Experiment III-6

Temperature

We are all familiar with hot and cold because of nerve sensors which detect the gain or loss of heat from our skin.  But those sensors only provide a rough estimate of how hot or cold our surroundings are.  To more precisely measure of the degree of hotness or coldness a number of people have invented instruments and accompanying definitions.

Generally objects expand when they are heated and contract when cooled.  Different materials have different rates of expansion.  By comparing the expansion of two different materials, it is possible to formulate a measure of temperature.

The first commonly used temperature scales were devised to measure the weather.  In 1701, the Danish Ole Christensen Rømer (b1644, d1710, portrait right→) created one of the first practical thermometers using red wine in a glass container.  For a given temperature rise, the wine expands more than the glass so that the wine's meniscus in the narrow neck of a glass container will rise noticeably.  Rømer created a temperature scale for the neck of the glass container such that with the thermometer immersed in a mixture of salt and ice, the meniscus was marked as zero and when in boiling water, it was marked as 60.

Daniel Gabriel Fahrenheit (b1686, d1736, ←portrait at left) devoted most of his life to creating precision meteorological instruments in Amsterdam.  After meeting Rømer in Copenhagen, in 1714 Fahrenheit substituted mercury in his glass thermometer.  Fahrenheit thought it would be practical to use a scale in which 0 corresponded with the coldest temperature normally encountered and 100 corresponded to the hottest temperature.  Fahrenheit, being an instrument manufacturer realized the importance of not only choosing two easily obtainable calibration temperatures, but a scale which could be marked by repeated division of the space between the calibration temperatures.  He initially used a mixture of salt and ice as 0 and the temperature of the human body (held in the mouth or under the armpit of a living man in good health) a value of 96.  (One degree is obtained by dividing the separation in half 5 times, and by three once.)  Fahrenheit later increased the range of his temperature scale by assigning boiling point of water a value of 212.

Réne Antoine Ferchault de Réamur (b1683, d1757) created in 1731 a scale in which 0 represented the freezing point of water and 80 represented its boiling point. The Réamur temperature scale became popular in France.

In 1742, Swedish Anders Celsius (b1701, d1744, ←portrait at left) created an inverted centigrade temperature scale in which 0 represented the boiling point of water and 100 represented the freezing point.  Two years later Carl Linnaeus (b1707, d1778) suggested reversing Celsius' temperature scale so that 0 represented the freezing point of water and 100 represented its boiling point.  The centigrade scale was adopted largely because of a paper by Celsius, Observations on two persistent degrees on a thermometer, suggesting the importance of reliable calibration temperatures, and reported on experiments showing that the freezing point of water is independent of latitude and atmospheric pressure.  Celsius also determined the dependence of the boiling of water on atmospheric pressure, and gave a rule for the determination of the boiling point if the barometric pressure deviates from a standard pressure.  As a result the centigrade temperature scale gradually became popular throughout the world. The units of the centigrade temperature scale were designated degree centigrade (°C).

Over a century later, William Thomson (Baron Kelvin of Largs, Lord Kelvin of Scotland, b1824, d1907, photograph right→) proposed in 1848 a thermodynamic temperature scale which assigned 0 to the theoretical coldest possible temperature, thermodynamic absolute zero, and used a unit size equal to one degree centigrade.  His scale was later named the Kelvin scale (°K).

Creating a similar absolute temperature scale to accompany the them more common Fahrenheit scale, William John Macquorn Rankine (b1820, d1872) proposed in 1859 a scale with 0 as absolute zero, but used the Fahrenheit degree for its unit size.  This Rankine scale is denoted by the symbol °R.

In 1948, the Ninth General Conference on Weights and Measures rename centigrade scale to Celsius (°C) in honor of Anders Celsius.  In 1954, the Tenth General Conference on Weights and Measures selected the degree Kelvin as the metric unit of thermodynamic temperature.  The conference defined the degree Kelvin by assigning the exact value 273.16°K to the triple point of water (where gas, liquid, and solid phases may coexist in thermodynamic equilibrium).  In 1967, the Thirteenth General Conference on Weights and Measures simplified degree Kelvin (°K) to just Kelvin (K). The conference redefined Celsius temperature as the thermodynamic temperature minus 273.15 Kelvin.

#### but what is temperature?

Knowing how to measure something isn't a guarantee that you have even a foggy notion of what is being measured!  While temperature seemed related to what we feel as warm or cold, the cause of that warmth or cold remained obscure until a careful Newtonian analysis of atomic theory.  And that required some confidence that this chemistry actually described reality.  Recall that chemistry evolved out of the secret witchcraft of Persian, Arab, and Egyptian alchemists rather than the observations, mathematics and Greek logic used by physics.  Until the 1905 mathematical analysis of Brownian motion by Albert Einstein, some prominent physicists regarded atoms as a chemist's unsupported fantasy.  But by the middle of the 19th Century, some physicists began consideration of the physical implications of what became known as the kinetic molecular theory (= theory of moving collections of atoms).

The kinetic molecular theory was originated and developed by Robert Boyle (b 1627, d1691), Daniel Bernoulli (b1700, d1782), James Joule (b1818, d1889), A. Kronig (b1822, d1879), Rudolph Clausius (b1822, d1888), and Clerk Maxwell (b1831, d1879).  It was found experimentally that the temperature of a gas (using the absolute Kelvin or Rankin scales), T, depends on the gas pressure, p, container volume, V, and number of contained molecules, n, by
pV = nRT.
R is a constant required because we arbitrary choose all measurement units.  (This is just like if we want to measure short times in seconds and long times in hours, then find there there is a mathematical relation between both:  we find we need to multiple the hours by the constant, 3600, to obtain the equivalent amount of seconds.)
J. Willard Gibbs (b1839, d1903, ←photo at left) and Ludwig Boltzmann (b1844, d1906, photo at left→) helped create statistical mechanics which included thermodynamics explaining such properties as temperature.  They assumed that pressure is due to the change of momenta of molecules striking the container walls.  Since molecules are randomly moving in three dimensions, the calculation combined the time between collisions (determined by 1/3 of the root mean-square speed), and momenta change (twice the average speed times the total mass given by n times molecule mass, M).
p V = 2/3 (1/2 n M vrms2), or by substitution
1/2 M vrms2 = 3/2 R T.
The left side of the equation is simply the calculation of the energy of motion of the molecules, and the right side is the gas temperature, adjusted by constants for the three dimensional geometry of our space, the amount momentum changes when things perfectly bounce, and our arbitrary choice of units.  So we have arrived at the conclusion that absolute temperature is a measure of the average kinetic energy of the randomly moving gas molecules.

### Experiment

We have discovered or created a variety of devices that respond to variations in temperature that can be adapted to observe and measure temperature.

Most materials expand to larger size when they get warmer.  A liquid with a large rate of expansion can be placed in a container with a low rate of expansion such as glass.  The top surface (meniscus) will rise in the container as the materials warms.  The change can be exaggerated by using more liquid but having a very narrow neck on the container.

A scale can be marked on the neck to allow measurements that can be compared with those from other locations and times.  One such scale marks zero at the temperature of melting ice, and 100 at the temperature of boiling water.  This was once called the Centigrade scale, but has been renamed the Celsius scale in honor of .... Celsius.

Some layered semiconductor crystals allow small amounts of electrical current to flow.  This electricity can be measured as the current flow (Amperage) or the energy driving the flow (Voltage).

We can gain assurance of the value of our devices by comparing the results of one device that the results from a different device.  This calibration process is particularly valuable for making a new device able to provide measurements that use a scale familiar to us.

### Procedures

1. Obtain two or more devices that provide variation with temperature.  One device might be a glass thermometer.  A second device might be an electronic temperature sensor or even the time required for a spoon of sugar to dissolve when stirred into a glass or water.  Many processes are temperature dependent and so can be utilized for temperature measurement.

2. Place the devices in an environment that likely provides a steady temperature such as a mixture of mostly crushed ice with a little liquid water.  Most devices take some time to acclimatize to a new temperature so take that into account.

3. When you are sure you have a result that represents the temperature, record the results from both devices in a table in your science journal.

4. Place both devices in common environments at other temperatures and obtain more measurements.

Information can be displaced in several ways.  Text narrative is useful for describing procedure so others could duplicate what you did.  But narratives are not very useful for noting changes in information or discovering patterns.  Usually it is more useful to record a series of measurements in a table.  Columns can be labeled with repetitious information such as which device provided the information and the scale units (such as °C, °F, seconds or Volts).  Rows can be used to collect related measurements such as from different devices while they were at the same temperature.

A graph is a visual way to present measurements (called data) that both reveals patterns and facilitates finding mathematical equations that precisely describe patterns.  This process is called curve fitting.  Computers can assist both the collection of measurements and the display and analysis of the information.  There are a variety of devices from companies like Vernier, MicroLAB, Pasco, and Texas Instruments that can collect information from a variety of electronic sensors.  They may immediately relay information to a more capable computer, or allow transfer late.  Vernier, MicroLAB, and offer computer software that are specialized for graphing and analyzing the data.  Microsoft and other companies offer business programs such as Excel that will graph and analyze data.  Because these are designed for business uses such are quarterly reports, they generally use default settings that are more cumbersome and need to be changed for this type of data.  (See directions on graphing.)

#### several simple measurements:

1. Gather temperature data from a variety of sources:  What is your body temperature?  Is the palm of your hand the same temperature as your foot or the inside of your elbow?

2. What is the room temperature?  Is the room temperature constant?

3. Put a tissue around the temperature sensitive part of the probe and hold it there with a rubber band.  Wet the tissue with water and note the pattern.  Is a constant or nearly constant temperature reached?  Is it different from the room temperature?  Does it make any difference whether the initial water was warmer or colder than room temperature?  Does it make any difference if a different liquid is used to wet the probe?

4. Record the measurements in your science journal and write a written report.  (Read what a report should include.)

#### patterns in temperature changes:

1. Connect the temperature probe to the box that interfaces with the computer, connect the interface box with the computer, then start the computer.  Launch the software designed to collect data.  (The interface box provides needed electricity to power the probe, received electrical signals back from the probe, and transmits it to the computer in an electronic format acceptable to the computer.)  Or alternatively, obtain any of a variety of other temperature measuring devices and prepare to measure the temperature at regular intervals of time.

2. Measure temperature changes that occur as time progresses of pure water cooling in a container surrounded by a mixture of drained crushed ice and table salt.

3. Construct a graph of temperature verses time.

4. Note if the water continuously cools.

5. Remove the pure water from the salt/ice mixture and record and graph the temperature of the pure water as it warms.

#### measuring high temperatures:

1. This is an investigation that limits measurement to devices that can themselves survive the high temperature.  Electronic temperature probes such as are sold by companies like Vernier, MicroLAB, Pasco, and Texas Instruments are ideal, but it is also possible to construct your own device if you have a way to measure small changes in Voltage or electric current.  (Research how to construct a thermocouple!)  Connect a thermocouple to the instrument amplifier inputs such as on MicroLAB's Sensor Amplifier Board.  Either measure the output of the instrument amplifier section to a portable Voltmeter or the MicroLAB interface box connected to a computer.  Measure the Voltage and use a calibration table to determine the temperature.

2. Measure the temperature at various locations in a flame.

3. Determine the temperature sideways across a flame and upwards to the region above a flame.  Where is the highest temperature in a flame?

4. Record your results in your science journal and write a report.

5. Solids glow at high temperatures; this is called black body radiation.  Note the visible color at various temperatures.

#### measuring small temperature effects:

1. This is another investigation where electronic devices do well.  Connect a temperature sensor to the instrument amplifier inputs of a device such as MicroLAB's Sensor Amplifier Board.  Connect a variable voltage from the bottom of the board to the inverting input (-) of the Instrument Amplifier.  Either measure the output of the instrument amplifier section to a portable voltmeter or the MicroLAB interface box connected to a computer.

2. Vary the Voltage to adjust the output to zero then turn on the amplifying resistance to make the temperature sensor more sensitive.

3. Measure the Voltage and the previous calibration of the probe to measure small changes in temperature.

4. Heats of solution.  Measure small changes in temperature due to addition of salts.  Either use software or an instrument amplifier on a Sensor Amplifier board to amplify the voltage.

5. Measure heats of reaction.  Measure small changes in temperature due to various chemical reactions.  Either use software or an instrument amplifier on a Sensor Amplifier board to amplify the voltage.

Hopefully by the time you read this you realize that there are a great many investigations which can be done involving temperature measurement.  The above only give a few suggestions to encourage you to be creative and to formulate your own investigation.  In all situations, be sure to consider the hazards which may be involved in your investigation and take precautions to assure safety.

Communicating technical information such as observations and findings is a skill used by scientists but useful for most others.  If you need course credit, use your observations in your journal to construct a formal report.

### References

created 25 January 2007
revised 12 July 2009
by D Trapp