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Flash Freeze

Given 2 beakers of water, which have the same physical properties, each contain the same amount of water at a uniform temperature. Beaker Hot has water at a temperature of $$t_H$$ and Beaker Cold has water at a temperature of $$t_C$$, where $$t_H > t_ C$$. We place the beakers in a freezer, which beaker would freeze first?

1) Beaker Hot
2) Beaker Cold
3) Both will freeze at the same time.
4) It depends.

Note by Calvin Lin
3 years, 1 month ago

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1 · 2 years, 7 months ago

Option 4. · 3 years, 1 month ago

If the temperature of the hot water is extremely hot, say at 1000 degrees Celsius it will lose much of its mass from the boiling of the water. After it has lost this mass, less energy must be lost by the liquid in order to freeze and thus speeds up the process of freezing. This can be seen by the equation

$$Q = mc\Delta T$$

If the cold water's temperature is much lower, say at 10 degree celsius, its mass will stay relatively constant and there will be no increased rate in cooling. In this case beaker hot should freeze first.

Now if the temperature of the cold water is 0.00001 degrees Celsius, and the temperature of the hot water is at 70 degrees Celsius, Beaker hot wont have the advantage of having its mass being lost due to boiling. Beaker cold will be required to lose a significantly smaller amount of energy than beaker hot in order to freeze and therefore should freeze first.

Therefore it depends on what temperatures $$t_c$$ and $$t_h$$ are. · 3 years, 1 month ago

Yea true... The question asks for which beaker will freeze first... That depends but Beaker Hot has a higher rate of freezing · 3 years, 1 month ago

Yes but even though it has a higher rate of cooling it wont necessarily freeze first. Its analogous to making Usain Bolt run a race against yourself but you have the advantage of being put 1m before the finish line whereas he has to run the full 100m. Even though he can travel distances at a quicker rate, he will lose because you only have to travel a very short distance. · 3 years, 1 month ago

Yup, that was exactly what i meant · 3 years, 1 month ago