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A 50 watt heater is major over kill for a 3 gallon tank, a 10 watt heater is more than enough for a tank that size. You will nuke your aquarium very quickly the first time the 50 watt heater sticks on, with a 10 watt heater if it sticks on the aquarium temp will only raise a degree or two.
The specific heat of water is 4.179 Joules per gram per degree Centigrade. The density of water is 1 gram per cubic centimeter, so one liter is 1000 grams. This means it takes 4179 Joules to raise one liter one degree Centigrade.
To raise the temperature of 1 gallon of oil by 1 degree Fahrenheit, it typically requires about 1,800 BTUs. This value can vary slightly depending on the specific type of oil, but 1,800 BTUs is a commonly accepted estimate for heating purposes.
It takes 8.33 BTU to raise the temperature of water 1 degree F.
q(Joules) = mass * specific heat * change in temperature q = 32.0 grams H2O * 4.180 J/gC *(54.0 C - 12.0 C) = 5617.92 Joules this is, of course 5.62 kilojoules
It takes 2.44 calories of heat to raise the temperature of one gram of ethyl alcohol by 1 degree Celsius.
The specific heat capacity of water is approximately 4.18 Joules per gram per degree Celsius. To raise the temperature of one kilogram (1000 grams) of water by one degree Celsius, it would require approximately 4180 Joules of heat energy.
"Calorie" comes to us from Latin "calor", meaning "warmth". A calorie is the energy required to raise the temperature of one gram of water by one degree centigrade.
This is a pretty straightforward calculation. By definition, a BTU is the amount of energy required to raise one pound of water one degree F. But you have one gallon of water, which weighs approximately* 8.34 pounds. So, you'd need 8.34 BTU to increase one gallon of water one degree F. Note how the amount of time was not important. Whether you heat the water slowly or quickly doesn't matter. You will still require 8.34 BTU to raise the temperature of a gallon of water one degree F. * I say approximately because the weight of water varies slightly with its temperature. Water is at its densest at 4 degrees Celsius (39 degrees F). A gallon of water at temperatures above and below that value will weigh less.
U.S.gallon = 8.33 pounds of water. Therefore to raise the temperature by one degree F will require 8.33 BTU. The initial temperature of 50 F is inconsequential.
A calorie is the amount of heat required to warm 1 gram of water one degree Centigrade. A Calorie spelt with a big "C" is a kilocalorie and is used in evaluating food energy. It is the heat required to raise 1 kilogram of water one Centigrade degree. On an energy basis a calorie is 41 840 000 ergs.