Hey Guys,
It's that time of the term again when all exams are popping up!!
I'm just wondering if you'd be able to help me with this maths question that I'm a bit stuck on.
What we have to basically do is find out whether a cup of coffee will stay hotter longer when the milk is poured in first, or when it's poured in after the hot water. Our teacher isn't too fussy on which option we got out in the end, he is just interested in the steps we took to come to that conclusion.
Anyway, I have recorded the temperature over a period of time for each coffee ie. (milk in first, and milk in last).
By using Newton's Law of Cooling (which we were required to use), I have found the equations for T(t) where T=temperature and t=time, for both the coffees.
I am now just wondering how do I show which coffee type decreases at a faster rate??
Any help will be greatly appreciated.
Thanks for your time.
Chantelle.
ouldn't it depend on the room temperature, and the initial temperature of the creame? And whether if you mixed last, is the creame now warmed up by room temperature, or is it at the same intial temp from the fridge?
http://www.mast.queensu.ca/~peter/investigations/18coffeecream.pdf
Hi Chantelle,
To determine which coffee type decreases at a faster rate, you need to compare the equations you found for T(t) for both coffees. By analyzing these equations, you can determine the rate of decrease for each coffee.
Here are the steps you can take to compare the rate of decrease:
1. Take a look at the equations you found for T(t) for both coffees. These equations should provide a mathematical representation of how the temperature changes over time for each coffee type.
2. Examine the coefficients and variables in the equations. Look for any similarities or differences that could affect the rate of decrease. For example, check if there are any common factors, constant terms, or variables affecting the rate.
3. Compare the coefficients or variables that directly affect the rate of decrease. If one coffee has a higher coefficient or variable value than the other, it suggests that it cools down faster.
4. Evaluate the rate of decrease for each coffee type. You can calculate the rate of decrease over time by differentiating the T(t) equations with respect to time (t). The resulting differential equation would show the rate of change of temperature with respect to time for each coffee. Then, you can compare these differential equations to determine which coffee cools down faster.
5. Analyze the results and draw your conclusion based on the comparison. If the rate of decrease is higher for milk in first coffee than the milk in last coffee, then it suggests that coffee with milk in first cools down faster.
Remember, it's important to consider other factors that might affect the rate of decrease, as you mentioned, such as room temperature and initial temperature of the milk. These factors could influence the overall cooling rate of the coffee and should be taken into account when drawing your final conclusion.
I hope this helps! Good luck with your math question and exams. If you need any further assistance, feel free to ask.