One of the pails contains 1 gallon and the other one has 3 gallons of water. The water temperature is the same in both.  Check the one that has more calories or heat energy. Explain your choice.

Expert Answers
gsenviro eNotes educator| Certified Educator

The amount of heat energy contained in a substance is a function of its mass, its temperature and its specific heat capacity. This heat energy can be calculated as:

q = m x c x T

where, q is the amount of heat energy contained in the substance of mass m, at a temperature of T. c is the specific heat capacity of the substance and is defined as the amount of heat required to raise the temperature of 1 unit of mass of the substance by 1 degree Celsius. 

Here, both pails have the same substance: water. Hence the specific heat capacity is the same in both cases. The temperature of the water is also same in both the pails. The only difference is the amount of water (1 gallon versus 3 gallons). Therefore, the pail with the higher quantity of water (that is, 3 gallons) will have a higher heat energy.

Another way to look at this is that it takes more heat to raise the temperature of 3 gallons of water as compared to 1 gallon of water. Thus, 3 gallons of water will have a higher heat energy content.

Hope this helps.