Pressure in the Diet CokeTM & MentosTM Reaction
Perform a series of experiments on the reaction between Diet CokeTM and MentosTM candies. Use the data to estimate what the pressure would be inside a sealed 2 L bottle of Diet Coke with 5 Mentos mints.
Your plan should include the following information, but in your own words.
- Make a Diet Coke & Mentos fountain.
- Set off your fountain & measure the height of the spray.
- Repeat with caps that have different size holes.
Write out your detailed procedure. Be sure to descrbe how you made the fountain (include a labeled diagram, the size of the bottle of Diet Coke, number of Mentos and how you attached them together, etc.):
and how you measured the height of the spray, using a ruler as a scale hypsometer.
(In the above example, the height of the spray would be 4.5m.)
Data & Observations
Here are data for one of my physics classes:
|Diameter of hole
|Area of hole
|Dist. to 2m mark
|Height of 2m mark
|Dist. to top of spray
|Height of spray
(You will need to calculate in the numbers for the area of the hole, height of the spray, and pressure.)
Calculate the pressure in each bottle using the equation P = ρgh, with ρ = 998 kg/m3, g = 9.8 m/s2, and h as calculated from your measurements. Use the data from your class. If you choose to leave out one or more data points, be sure to include an explanation!
Also calculate the area of each opening. For example, if the diameter is 4.0 mm, the radius is 2.0 mm, which means the area is πr2 = (3.14)(2.0)2 = 12.6 mm2.
For your error analysis, estimate the uncertainty (±) for your height measurement and multiply it by ρ and g to find the uncertainty in the pressure measurement. (There is also some uncertainty in the diameter of the opening, which we will ignore.)
Accurately plot a graph of pressure vs. the area of the opening. Each data point is the calculated pressure for that size opening. (If you have two data points for a given opening, calculate the average.) Your error bars should extend to the maximum and minimum given by your uncertainty (the ± value).
Draw a best-fit line and extrapolate to an opening of zero (0 mm) to find the pressure that would be present in a bottle with no opening.
An example graph with sample data is shown below:
In the above example, the pressure with no opening would be reported as (59 000 ± 5 000) Pa.
Because you are calculating the pressure with no opening as the y-intercept of your best-fit line, you must either:
- Calculate the y-intercept graphically, plotting your data points accurately on graph paper and drawing the best-fit line with a straightedge.
- Calculate the best-fit line and y-intercept statistically, using linear regression. If you do this, be sure to provide the slope, intercept, and correlation coëfficient.