Fahrenheit – Celsius Conversion Lab
Skills and Ideas:
1The scientific method
1Computing an average
1Computing a standard deviation (optional)
1Point-slope formula
Materials:
1A thermometer with Fahrenheit and Celsius temperature measurements.
1A small cup of ice water.
1A cup of room temperature water.
1A cup of heated water (preheated and brought in a thermos).
Background (to be included) – history of the Fahrenheit and Celsius scales.
A history of degrees Fahrenheit:
Fahrenheit is a temperature scale invented by and named after a German physicist, Gabriel Fahrenheit, who proposed it in 1724. In this scale, the freezing point of water is 32 degrees and the boiling point of water is 212 degrees.
According to Wikipedia, there are many competing stories as to the origins of the Fahrenheit scale. The first is that Fahrenheit made the zero of his scale equal to the lowest temperature he measured in his hometown of Gdansk in the winter of 1708-1709, and made 100 equal to the temperature of the human body. We know now that the normal human body temperature is 98.6 degrees Fahrenheit. This discrepancy might be explained by a number of things: Dr. Fahrenheit could have had a fever during his experiments (not unusual in a cold winter), his measurements could have been inaccurate, or he could have measured the temperature of a cow, which runs slightly higher than that of a human.
A second story theorizes that Fahrenheit simply used an older scale made by the Danish astronomer Ole Rømer, at which water freezes at 7.5 degrees. He then multiplied by 4 to eliminate fractions and increase the sensitivity of the scale. He then calibrated his scale between the freezing point of water and normal human body temperature, which he took to be 96 degrees, so there would be exactly 64 degrees between them. This would allow him to make all the marks in between on his instruments simply by subdividing the distance eight times.
Another less well-known theory is that Dr. Fahrenheit was a Freemason. In Freemasonry, there are thirty-two degrees of enlightenment. The use of the word 'degree' is theorized to come from the degrees of Freemasonry. No conclusive evidence exists to support this theory, but neither is there any against it, so the story persists due to the large number of possible coincidences.
A history of degrees Celsius:
The Celsius temperature scale is named after the Swedish astronomer Anders Celsius (1701-1744) who proposed the system. From its inception until 1954, the scale was defined such that 0 degrees Celsius was the melting point of ice and 100 degrees was the boiling point of water at one atmosphere of pressure (one atmosphere is defined as the average pressure at sea level, actually defined by the pressure in Paris). It has since been updated around two other points, absolute zero and the triple point of water at one atmosphere (though ice still melts at very close to 0 and water boils at almost exactly 100).
Absolute zero is defined to be the lowest possible temperature, at which no heat remains in an object. The triple point of any substance is the temperature and pressure at which the substance can exist as a solid, liquid, or gas.
Temperature is measured in degrees Celsius in many scientific settings in the United States. In many countries, it is the everyday measure of temperature.
Averages
LeBron James averaged 31.4 points for the 2005-2006 season (Wikipedia). What does that mean? How is that calculated?
If a player scores 11 points in the first game of the season, and 5 points in the second game, what is his scoring average after the first two games?
More generally, what is the average of two numbers a and b?
If a player scores 5 points in the first game, 9 points in the second game, and 21 points in the third game, what is her scoring average?
Can you find a formula for the average of N numbers?
Point-Slope Formula
The slope-intercept form of the equation of a line is the familiar y = mx + b equation, where m represents the slope of the line and b represents its y-intercept. This is sufficient to define the line, but how would you figure out the equation of a line if you were given only two points?
Can you find the slope of the line that runs through the points (1,3) and (3,7)?
Slope can be calculated by rise over run, using just the points given. But finding the y-intercept can be a little tricker. One way to solve this problem is to use a different representation of the line. We can write the equation of a line point-slope form. Just as the name suggests, all you need is the slope and a point on the line. The point-slope form of a line is: y – y0 = m( x – x0). Here, (x0, y0) is any point on the line.
Earlier, you calculated the slope of the line between (1,3) and (3,7). Plug in the point (1,3) to the point-slope formula and convert that formula into slope-intercept form.
Now do the same thing, but this time plug in the point (3,7). What do you notice about the two slope-intercept equations?
What does this tell you about what point you have to put in for (x0, y0) in the point-slope form?
Lab Procedure –
1Measure the temperature of the cup of ice water using the thermometer. Let each student try and read the thermometer by his or her self, and take the average of the readings.
1Draw a graph with the x-axis measuring degrees Fahrenheit and the y-axis measuring degrees Celsius.
1Plot the measurements of the first cup of water on the graph.
1Pour out some of the heated water into a cup and measure the temperature in a similar fashion. Compute the average of the measurements and plot it on the graph as well.
1Connect the two points with a line, then find the slope of that line using the point-slope formula.
1Use the thermometer to measure the temperature of the room-temperature water. Tell the students the measurement in Fahrenheit, but not in Celsius. Have them use the formula for the line to figure out what the Celsius temperature should be. Confirm this by checking the thermometer.
1Compare your formula to the actual formula for Fahrenheit-Celsius conversion.