How much energy would be lost to the environment if a pond containing 2.3E12 kg of water at 22 degrees Celcius completely freezes?
The Specific Heat Capacity is a measure of the amount of heat needed to raise or lower the temperature of a substance by one degree Celsius. For water, the Specific Heat Capacity (C) is given as 4.184 Joules per Gram degree Celsius, or C = 4.186 j/gc.
The formula relating Specific Heat Capacity, Temperature, and Mass is given as:
Q= MC(Tf - Ti), where
Q = the amount of heat energy gained or lost in Joules,
M = the mass of the substance,
C = the Specific Heat Capacity of the substance,
(Tf - Ti) = the change in temperature of the substance.
It's necessary to express the mass in terms of grams, not kilograms. We know the mass of the pond to be 2.3 * 10^12 Kilograms, which is the same as 2.3 * 10^15 grams.
Q= (2.3*10^15 g) (4.186 j/gc) (22 c - 0 c) = 211.811 * 10^15 J
Q= 2.12 * 10^17 Joules,
so to freeze the whole pond, quite a bit of heat is lost to the environment.