Let’s use the following equation to determine the amount of heat energy that is required to increase the water’s temperature from 20˚ to 100˚.
Q = mass * specific heat * ∆T
Q = 3 * 4190 * 80 = 1.0056 * 10^6 J
For a stone, ∆T = 550 – 20 = 530
Q = 1 * 800 * 530 = 424,000 J
To determine the number of stones, divide these two numbers.
N = 1.0056 * 10^6 ÷ 424,000
The answer is approximately 2.37 stones. If you use 3 stones, some of the water will boil. I would use 3 stones to make sure that water’s final temperature is 100˚C.
Native Americans boiled water by adding very hot stones to a leak-tight water vessel.?
What minimum number of 1.0 kg stones at 550 ∘C must be added to a vessel holding 3.0 kg of 20∘C water to bring the water to a boil? Use 800 J/(kg⋅K) for the specific heat of the stones and 4190 J/(kg⋅K) for the specific heat of water.
- t1s = initial temperature of a stone = 550 °C
t2s = final temperature of a stone = 100 °C
t1w = initial temperature of the water = 20 °C
t2w = final temperature of the water = 100 °C
ms = mass of a stone = 1.0 kg
mw = mass of the water = 3.0 kg
cs = specific heat of a stone = 800 J/(kg⋅K)
cw = specific heat of water = 4,190 J/(kg⋅K)
Qs = energy lost by a stone = to be determined
Qw = energy gained by the water = to be determined
n = number of stones needed to boil the water = to be determined
NOTE: Since the temperatures involved are about DIFFERENCES in temperature,
there is no need to convert Celsius temperatures into their Kelvin equivalents.
Qw = mw∙cw∙(t2w - t1w)
Qw = 1,005,600 J Energy gained by the water
Qs = ms∙cs∙(t2s - t1s)
Qs = -360,000 J Energy lost by a stone
n = |Qw| / |Qs|
n = 2.793333333 stones, rounded up to 3 stones20
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