How can I calculate the energy required to cause a temperature rise?

1. What is the unknown? Your problem asks "How much energy...?" The units aren't specified, but since you spot 'calories' in the given information, it will probably be easiest to get your answer in calories.
2. What information is given? You know that:
   • the specific heat is 1.0 cal/g°C
   • the mass of water is 25.1 g
   • the temperature change is 72.0°C
3. How is the information in the problem related to the unknown? The relationship between heat and temperature change is

   heat = mass × specific heat × temperature change

4. Do the math. Now you're ready to do the calculation itself:

   heat = (25.1 g)(1.0 cal/g°C)(72.0°C)

5. Is the final answer in the correct units? You want only calories. All other units should 'cancel' in the calculation somewhere.
6. Is the size of the answer reasonable? Your reasoning should go something like this: The specific heat means that it takes 1.0 calories of heat to warm 1 g of water up by 1°C. So it should take 25.1 calories to warm up 25.1 g of water by 1°C. And it should take 72.0×25.1 calories to warm up 25.1 g of water by 72.0°C.

   You can also check the answer by working the problem backwards. For example, take the calories just calculated and divide them by the temperature change and the grams of water; do you get a specific heat of 1.0 cal/g°C?

Author: Fred Senese senese@antoine.frostburg.edu