Okay, so we start with the following question:
Find out how long it would take to bring Lake Erie to a boil given the total energy consumed in the United States in ONE year.
To start we need to find the following information:
483 cubic kilometers
1.0 gram/cubic centimeter
4.18 J/(gram*degree Celcius)
~20 degree Celcius
We are assuming that the TOTAL energy consumed by the United States in one year is COMPLETELY transferred to HEAT, thus raising the temperature of water (to a boil).
The 1st thing that should come to mind is the relationship for increasing the temperature of state of matter (solid, liquid, etc) given an added amount of heat, Q. The equation is: Q = mc(Tf - Ti).
We know that if we add heat, Q to an object its temperature will change by "delta T".. The energy consumed in the U.S. is essentially the work produced by the U.S. in a year. If all this WORK is COMPLETELY transferred to HEAT we can say Work, W, is equal to Heat, Q. Thus, W = Q.
The reason for this is imperative because the amount of energy produced in the U.S. per year is known commonly as "Power". Power is the amount of work performed in a given amount of time. It is expressed by the equation: P = W/t
If we take the three equations we have (for Heat and Power) we can solve for the time, t.
P = [mc(Tf-Ti)]/t
t = [mc(Tf-Ti)]/P
It's just simple algebraic manipulation.