I am going to measure how long it takes to get an ice cube to boil, followed by two cubes, then three, and so on up to 30. I will ensure that the pot I use is cool before starting each test. I will start the timer as soon as I turn on the heating element, after I put all the necessary ice in the pot, and stop the timer once the water comes to a heavy boil. I expect to see a positive relationship with how much ice there is, and how long it takes to boil, although I expect that once I start getting multiple layers of ice, the amount of time required will increase.



Cubes
Time (In Minutes)
1
1.80
2
2.25
3
2.58
4
2.75
5
2.80
6
3.17
7
3.48
8
3.97
9
3.98
10
4.10
11
4.42
12
4.77
13
5.00
14
5.07
15
5.47
16
6.27
17
6.77
18
6.25
19
6.63
20
6.80
21
7.13
22
6.78
23
7.18
24
7.60
25
8.02
26
8.67
27
9.13
28
9.42
29
9.67
30
10.12
Std. Dev.
2.35
Boiling Ice.png

Correlation coefficient = 0.9924

Coefficient of Determination: R^2 = 98.5%

Least Squares Regression Equation: y = 0.269 + 1.5651

I was expecting to a see a positive relationship in how long it would take to boil ice cubes, but I wasn't expecting such a close fit in times. Clearly, this experiment indicates that there isn't so much a matter of how much ice is used, but how much water is being heated to a boiling point.
It does seem that when there got to be more than one layer of ice cubes in the pot, the time required to boil became somewhat more erratic, but still holds fairly tight to the LSRE line.

As far as confounding influences go, the most obvious is that not all ice cubes are the same size, even when being drawn from the same set of ice trays.
Another factor is the air density inside the individual ice cubes, as the temperature of gases increase quicker than those of solids, this will affect the rate of the ice melting, therefore destabilizing the ice into liquid water, and liquid water into steam as it gets closer to a boiling point, thus varying the time required to get an ice cube to boil.
One more factor is the heat intensity on the pot, regardless of what is being used for a heating element (in my case, a gas stove), there is no guarantee that the heat from the element is being applied evenly at any given time, as well as how centered the pot is centered over the element, all of which will affect how much heat gets to the ice.

Despite the influences, I stand by my initial analysis in that how much ice there is in the pot, directly relates to how long it take for the ice to become water, and then to reach its boiling point.