# Experimenting whether the diameter of a pot affects boiling time for water

• swnsy05
swnsy05
Homework Statement
I'm experimenting for a school project if the diameter of a pot affects the time it takes to boil water in it. Does what I have done sound correct? Does my model sound alright?
Relevant Equations
g(x) = c/(1+ae^(-bx))
Hey guys, I'll try to be as direct as possible. So for school i'm doing an experiment at home trying to find out if the diameter of a pot affects the time it takes to boil water inside the pot as it says in the title. I had three different pots with three different diameters. I got half a liter of water and made sure it was the same temperature each time before starting to boil it. I also measured 500 g of water aka 0.5L on an electric scale to be as precise as possible. I also used a thermometer thing connected to a multimeter to get an accurate reading of temperature. Then I placed the smallest pot on the induction stove and took the time from I turned on the stove till the thermometer reached 100 degrees. I saw that the smaller diameter the longer it would take to boil the water which makes sense. The bigger the diameter of the pot the more area the pot can absorb heat from from the induction stove right?

So then I had three points, (Diameter 1, Time1) (Diameter 2, Time2) and (Diameter 3,Time3) and I plotted it into Geogebra and did a regression analysis. I selected a logistic graph since that's what looked to fit best. Is that wrong? It fitted perfectly on the three points I made and none of the other models were as good as the logistic one. So then now I have a model to find the time it will take to boil water given we know the diameter. To test if this model was good I took a fourth pot which I measured the diameter on and calculated the projected time it would take to get water to boil. If I remember correct the Diameter was 14cm and the projected time was one minute and 57 seconds. Then when I tried it in real life it took 1 minute and 20 something seconds. I thought about it and it must have been because the new pot was thinner than the other ones right? But how can I explain that from a physics standpoint? That since it was thinner a bigger portion of the energy could go to heat the water instead of the pot compared to the other ones that were thicker on the bottom. Or is that wrong?

Another thing i'm wondering is how would it be with uncertainty? The measuring tape I used to find the diameter had millimeters precision. So I got the measurements of Smallest pot : 10.5 cm, medium pot : 15.7 cm and larger pot 17.7 cm. So would I write then in my rapport for example (10.5 +-0.1)cm? And for the temperature, the rig I had to the multimeter capped out at 99 degrees Celsius. So +-1 degree? I'm not that good with the uncertainties it's something I have always struggled with but how would it be with my model then? The model I got from regression was the logistical model given by g(x) : 81.12818 / (1-5.47591 * e^(-0.20477x)) Where I let x be the diameter to get the time projected. Have I done anything wrong so far? I was supposed to find the link between diameter and time it takes to boil so I did the measurements and found the logistic model. Have I made any mistakes? Was my thinking about why the fourth pot took less time correct? Does the model look correct? For context the actual measurments I got for the boiling times and diameters were Pot 1: Diameter = 10.5cm, time = 224 seconds. Pot 2: Diameter = 15.7cm, time = 104 seconds. Pot 3: Diameter = 17.7 cm, time = 95 seconds. And for the fourth pot which isnt on my model but it was to check if my model was correct was 14 cm and it took 89 seconds to boil. I appreciate any help / advice / comments

So you think that if the diameter is less than 8 cm, the time will be negative?

You have 3 points and 3 adjustable parameters, of course you get an exact fit!

swnsy05 and Orodruin
And on top of that you have measurement error, possibly different ability to heat using induction on different pots (induction stoves heat pots using magnetic fields, not by heat conduction), possibly different efficiencies in different parts of the induction surface … the error sources are numerous.

swnsy05
mjc123 said:
So you think that if the diameter is less than 8 cm, the time will be negative?

You have 3 points and 3 adjustable parameters, of course you get an exact fit!
Thanks for your reply. You're right it doesn't make sense with negative time. Would you suggest a linear regression then?

Orodruin said:
And on top of that you have measurement error, possibly different ability to heat using induction on different pots (induction stoves heat pots using magnetic fields, not by heat conduction), possibly different efficiencies in different parts of the induction surface … the error sources are numerous.
Thank you for your reply. You're right there are numerous error sources like that. The pots are all of the same material though and they are places on the same stove. If we assume the pots are identical except for the diameter which they pretty much are except for the last one and we assume the efficiency is the same are there any other MAJOR error sources I should account for? This is a high school level project, I have tried letting all the pots etc be as equal as possible.

My suggestion is that you plot all four points on a graph and look at the graph. See what, if anything, you can infer from that.

Mister T said:
My suggestion is that you plot all four points on a graph and look at the graph. See what, if anything, you can infer from that.
I remember seeing a plot with 3 not 4 points, but it's no longer there.

My first guess would be a simple power law behavior ##t = Ar^k## with ##A## and ##k## being unknown constants. In a log-log plot, such a relationship is a straight line as
$$\log t = \log A + k \log r$$

kuruman said:
I remember seeing a plot with 3 not 4 points, but it's no longer there.
In the OP he mentions a fourth point.

Mister T said:
In the OP he mentions a fourth point.
That is true. However, the plot had 3 points. See @mjc123's comment in post #2 about fitting 3 data points with 3 variable parameters.

kuruman said:
That is true. However, the plot had 3 points. See @mjc123's comment in post #2 about fitting 3 data points with 3 variable parameters.
I know. But he has 4 data points. He should plot all 4.

Here is a plot of all 4 with a second degree polynomial to the first 3 points with three adjustable parameters (OP had a logistic fit). OP recorded the fourth point (square marker) to test whether it would be consistent with the first three. It does not appear to be so and that's where we are now.

That fourth pot could be made of a different metal or alloy.
That could change both its electrical resistance and its thermal conductivity.

Tom.G said:
That fourth pot could be made of a different metal or alloy.
That could change both its electrical resistance and its thermal conductivity.
This is the most likely cause to be honest. Changing any variable other than the radius is likely to introduce additional dependence. For example, a cast iron pot will give significantly better heating than a wooden pot. All pots are not born equal.

A much more reproducible experiment would be to take a single pot with a lid with a hole in it, and change the size of the hole. You can take a single sheet of appropriate material (if it's plastic, make sure it won't melt or deform at boiling temperatures) with a hole in it that you make bigger and bigger.

Where was the temperature measured in the experiments? Was the placement of the thermocouple consistent in all 3 cases (i.e., the same distance above the bottom)? How do you know that the induction heating rate of the pots was the same in all the cases? Would placing all four pots on the same "burner" of the stove given different results?

In the end, the rate of heat flow per unit area at the bottom of the pan will determine the water temperature vs time at the bottom.

Lord Jestocost

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