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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?

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2 Answers

up vote 6 down vote accepted

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.

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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.

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Sorry, I didn't specify that I used an electric kettle. From your explanation, it seems that you are talking about a stove top kettle, is that correct? –  Hannah Andersen May 21 '13 at 10:18
    
@HannahAndersen: It would work for any kettle that is made of metal. –  Manishearth May 21 '13 at 10:54
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