Why is it faster (as in proportion to volume) to boil 4 cups of water than to boil 2 cups? I did an experiment where I boiled two cups (500ml) of water in a kettle, and it took 1:30 minutes to reach around 98 C, average. However, when I boiled 4 cups of water, (1L) it only took me 2:30 minutes, when I expected it to be 3:00 minutes. Does this mean that the more water I boil, the faster it will reach 100 C (proportional to its volume, of course)? The kettle and the thermometer used were cooled down first before boiling another batch of 24.5 C water, and I did a few trials.
Can you tell me the reason for this? And is there an equation I can use, to figure out, for example, how long it would take to boil 6 cups? 
 A: Double the ammount of water does not need doulbe the ammount of time to heat, since while the energy needed is doubled indeed, losses due to vaporization and radiation from the kettle should be approximately constant.
You can plot the time needed for a given ammount of water to boil and try to fit a function into that. With two data points you can manage to fit a straight line, corresponding to linear growth, although I do not expect that to be a good fit. Try doing measurements with 1, and 3 cups, too. Then you have more data and see what kind of function fits the data best. That way you can extrapolate to higher ammounts.
A: The simplest explanation that I haven't seen in another answer yet is the following:
You're not just heating the water
While the heat capacity of water is very large, your kettle also has a heat capacity and the parts of it in contact with the water also need to be heated. The heating element itself needs to be heated to an even greater temperature in order for the water to attain, on average, a temperature of 98 degrees Celsius.
A: Simply because the rate of flow of heat slightly increased when you added more water:
Heat is transferred very quickly to the kettle (which I assume is made out of metal), as metal is a good conductor of heat. Air is a bad conductor, so no heat enters the water through the air. Water is a worse conductor of heat than metal (it also has a pesky habit of absorbing the heat instead of transmitting it). This means that the metal has a lot of heat to give to the water, and the water takes it in at a relatively slower rate. Also, the water can only receive heat directly from the metal. So, increasing the surface area of water in contact with the metal increases the rate of intake of heat (and the efficiency of intake; with the initial system only the water near the lower surface will be heated, and the lowered temperature gradient will slow further intake of heat until the heat spreads out). Since the "time taken to boil will be double" only works if the rate of intake of heat is constant, this accounts for the discrepancy.
A: I regularly use boiling water as a timer. I set my whistling tea kettle to boil first thing in the morning, then go to the bathroom to brush my teeth and wash my face. I know that if I put 3 cups in the pot, I have approximately six minutes to complete my washing up; if I use 4 cups, I have 8 minutes. So, about 2 minutes per cup of water. (I always measure the water by cup when adding to the tea kettle, because I like my tea to have a consistent strength.)
The general rule seems to hold with an open sauce pan as well. I often have to boil one cup of water for a recipe; it takes two minutes. 
It doesn't seem to matter whether it is winter or summer. My house is very close to sea level.
The reason that I know how long it takes is that I have a problem with walking away from an open pot of water and forgetting about it since it doesn't have a whistler. So I began setting the stove timer when I put on a larger pot of water for pasta. 
The reason I found my way here, is that my boyfriend has started making tofu from scratch, which involves bringing raw soy milk to a boil and then holding it at boiling for 30 minutes. Soy milk burns and sticks easily. So I recommended a double boiler. He makes very large batches. So he is trying to boil 2 gallons of soy milk within an outer pot with a 4-gallon capacity. He stood around for a very long time waiting for it to boil and then got impatient and stopped the experiment after 50 minutes.
But I estimated that it probably would take over 90 minutes for the soy milk to come to a boil, based on my 2 minutes-per-cup rule, because he knows that he put one gallon of water in the outer pot. My calculation is 16 cups per gallon = 48 cups x 2 minutes per cup = 96 minutes. This may be off by a lot, since I don't know how the double boiler setup affects the time it takes, nor do I have experience with these larger volumes. (I assume that the soy milk will eventually boil in a double boiler, but I have not been able to find any evidence of that on the web.)
While waiting for more answers and data, I sent him a thermometer. :)
A: When you heat the water it evaporates.. measure your 4 cups after it’s reached your desired temperature for your experiment and see if you still have the same volume. 
