Determining which coffee has a greater rate of cooling

In summary, the conversation revolves around determining the fastest rate of cooling among three different cups of coffee by modeling their cooling using an exponential function. The difficulty lies in determining the slope of the graphs at a common point, as they do not all start from the same point. The solution suggested is to calculate the slope at a specific temperature for each graph. However, there is a question about whether the relationship between the derivative of the graphs will change and if this method can accurately determine the fastest rate of cooling.
  • #1
nousername
31
1
Hey,

I have this math investigation task which asks us to model the cooling of coffee in three different cups over a period of time. Anyway, i got the data, did a scatter plot and found the exponential model, but i don't know how i could determine which one has the greatest rate of cooling.

I know that I need to look at the slope, but they don't all start from the same point on the graph, so i can't determing which one has the fastest rate of decay. If they all started from the same point i would be able to see the different functions branching off from that point, and if one has a steeper slope than the other i would know, but this wasnt the case. Can someone please help! Thanks.
 
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  • #2
Calculate the slope at a common point. For example, take the point 40° at every coffee and calculate the slope at that point.
 
  • #3
Hey thanks man. Do you know if the relationship of the derivative of the three graphs will change. So if i measure the derivative of each graph at some temperature (remember it's exponential) and find that one graph has a steeper slope than the other... could that change? so the other graph will now have the steeper slope? Because if that is true, then we can't use that to determine which graph has the fastest rate of cooling overall. Thanks.
 

1. What factors affect the rate of cooling in coffee?

The rate of cooling in coffee can be affected by several factors, including the temperature of the environment, the type of container the coffee is in, the volume of coffee, and the type of coffee beans used.

2. Does the size of the coffee cup affect the rate of cooling?

Yes, the size of the coffee cup can affect the rate of cooling. A larger cup will have a larger surface area, allowing the coffee to cool faster compared to a smaller cup.

3. How can we accurately measure the rate of cooling in coffee?

To accurately measure the rate of cooling in coffee, you can use a thermometer to track the temperature of the coffee over time. Take temperature readings at regular intervals (e.g. every 30 seconds) to get a more precise measurement.

4. Does the type of coffee bean affect the rate of cooling?

Yes, the type of coffee bean used can affect the rate of cooling. Different types of beans have different densities and moisture levels, which can impact how quickly they cool down.

5. How can we control the variables when determining the rate of cooling in coffee?

To control the variables, make sure to use the same type of coffee beans, same volume of coffee, and the same type of container for each cup of coffee. Keep the cups in the same environment and measure the temperature at the same intervals for each cup.

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