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.
## No comments:

## Post a Comment