Stored Energy Calculations

QUESTION: How hot will 2 cups of water get from 2 minutes in a microwave oven?

                                     Joules
     Specific Heat of Water = 4180 -----------
                                   Kg - Deg. C

     Power of Microwave = 750 Watts

             Joule
     Watt =  ------
             Second

     Weight of Water = 0.454 Kg

     Time of Heating = 120 Seconds

You want to write an equation so the units cancel and you are left with degrees C. The Specific Heat of Water has Deg. C in the denominator, so we will have to divide by it.

                         Kg - Deg. C 
  X Deg. C = something * -----------
                         4180 Joules

"X" will be the increase in temperature (in degrees Celsius) we expect to see from applying the facts above. "something" has to have Kg in the denominator, so:

                              Kg - Deg. C      1
  X Deg. C = something else * ----------- * -------
                              4180 Joules   0.454 Kg 

Now we need to cancel Joules, so let's multiply by what a watt is:

                              Kg - Deg. C      1       Joule/second   
  X Deg. C = another thing *  ----------- * -------- * ------------
                              4180 Joules   0.454 Kg      Watt
 

Another way to write that is:

                              Kg - Deg. C      1          Joule
  X Deg. C = another thing *  ----------- * -------- * ------------
                              4180 Joules   0.454 Kg   Watt*second
 

Joules and Kg cancel out; now let's get rid of Watts and seconds in the next step:

              Kg - Deg. C      1          Joule
  X Deg. C =  ----------- * -------- * ------------ * 750 Watts * 120 Seconds
              4180 Joules   0.454 Kg   Watt*second

All the units now cancel on the right hand side of the equation leaving Degrees Celsius. So the answer is : 750 * 120 / 4180 / 0.454 = 47.425 Degrees Celsius increase in temperature! In the real world, "your mileage may vary." Try and think why that could be.