- #1

swnsy05

- 6

- 1

- 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 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