Charles Law “The Discovery of Natures Natural Temperature Scale”

Experimental Design Attach the capillary tube with the free floating mercury plug (which is sealed at one end and open at the other end) to a typical Celsius calibrated thermometer. Attach the capillary tube with the free floating mercury plug (which is sealed at one end and open at the other end) to a typical Celsius calibrated thermometer. Position the capillary tube so that the sealed end stands opposite to the -20°C mark on the thermometer. Position the capillary tube so that the sealed end stands opposite to the -20°C mark on the thermometer. Measure the volume of the trapped gas by reading the placement on the bottom of the plug on the adjacent thermometer. Since the capillary tube is placed at the -20°C mark you must add 20 to the volume of the gas. Since the tube is a cylinder and therefore has a constant cross sectional area and since V = (area)(height) we can use the height of the plug as a measure of the volume. Measure the volume of the trapped gas by reading the placement on the bottom of the plug on the adjacent thermometer. Since the capillary tube is placed at the -20°C mark you must add 20 to the volume of the gas. Since the tube is a cylinder and therefore has a constant cross sectional area and since V = (area)(height) we can use the height of the plug as a measure of the volume. Place the system into three different temperature baths and record the volume as a function of the changing temperature. Place the system into three different temperature baths and record the volume as a function of the changing temperature. Graph the behavior of the system using T as the independent variable and V as the dependent variable. Graph the behavior of the system using T as the independent variable and V as the dependent variable. Analyze the results and then discuss the outcome in terms of “Natures Natural Temperature Scale.” Analyze the results and then discuss the outcome in terms of “Natures Natural Temperature Scale.”

A Magic Moment of Math... A Magic Moment of Math... You can see by Mr. You can see by Mr. Zachmann’s fantastic diagram to the right that the graph of V vs Height is a DVM. Which graph represents the capillary tube with the greatest cross sectional area? ….Yes, the pink graph is correct. Now, since every measurement has random error associated with the reading which capillary tube minimizes the random error associated with the reading of the volume of the gas? … Yes, the bottom blue graph minimizes the error. For the same volume, the blue graph provides the greatest height. The relative error is the error in the measurement divided by the height. The blue graph gives the smallest ratio and therefore the smallest error. (REM: significant figure lessons and error genres)

Data: Room Temperature The wide angle picture (left) shows Mr. Zachmann suspending the system in room temperature water. The picture to the right zooms in on the readings. The temperature was 22.5°C and the volume of the gas was = 57.5 units.

Data: Cold Conditions Here the system is suspended in an ethylene glycol solution that was taken from the freezer. The picture to the left shows the temperature to be -10°C. The picture to the right shows the volume of the gas to be = 60 units.

Data: Hot Conditions The picture to the left shows the temperature of the hot water to be 88.5 °C. The picture to the right shows the volume of the hot gas to be = 81.5 units.

Data Analysis: Scatter Plot The dots on the graph are difficult to see but they seemed to be linear. When we connected the dots we were relatively sure a linear relationship was in play. The little bend in the data indicated we did suffer a little error. In the next slide linear regression was applied to the data. The result of that action presented for evaluation the “best fit” line that the data could present.

The DVM dream becomes a nightmare. The left graph displays a beautiful line but is has a horrible intercept… no DVM. The right graph shows the x-intercept to be very close to -273°C. At this junction we started to think that nature has her own natural temperature scale. Go to the next slide for the reasoning.

Movement: The Physical Basis for Natural Temperature From the previous slide it was clear that the empirical (experimental) relationship predicts a point where the gas does not claim any volume due to its aggressive behavior (AKA collisions). From our heat unit we learned that temperature as well as heat are tied to kinetic energy (KE = ½ mv 2 ). From this equation we can easily see why nature elects to use -273°C as her true zero. Since we don’t want to mess with Mother Nature we developed a new scale (called the Kelvin scale or Absolute scale) which reads 0 at -273°C. When we re-graph the data in Kelvin we get a beautiful direct variation (DVM) law known as Charles Law. It is important for you to remember that all gas laws which involve temperature require the temperature to be in Kelvin. A very common student error is to try to use Celsius rather than Kelvin. Most standardized tests present answers with this common error so be very careful…. From the previous slide it was clear that the empirical (experimental) relationship predicts a point where the gas does not claim any volume due to its aggressive behavior (AKA collisions). From our heat unit we learned that temperature as well as heat are tied to kinetic energy (KE = ½ mv 2 ). From this equation we can easily see why nature elects to use -273°C as her true zero. Since we don’t want to mess with Mother Nature we developed a new scale (called the Kelvin scale or Absolute scale) which reads 0 at -273°C. When we re-graph the data in Kelvin we get a beautiful direct variation (DVM) law known as Charles Law. It is important for you to remember that all gas laws which involve temperature require the temperature to be in Kelvin. A very common student error is to try to use Celsius rather than Kelvin. Most standardized tests present answers with this common error so be very careful….