You're heating a cup containing 8.00oz of water in a microwave.

you're heating a cup containing 8.00oz of water in a microwave. It takes 20.00seconds to heat the water from 20.0C to 70.0C. What is the approximate power rating of the microwave in kilowatts? Assume the cup has a heat capacity of 10.0J/C.


Thank you!!!

heat total = heat gained by water + heat gained by cup.

so..
Qtotal = (m Cp dT) water + (m Cp dT) cup

and if you notice..
the typical units of m are grams and Cp are J/g°C.. .so m x Cp = g x J/g°C = J/°C
which is the units for the heat capacity of the cup...
ie.. that 10.0J/°C = m x Cp cup !

so..
Qtotal = [(8.00oz x 1gal/128oz x 3780mL/gal x 1g/mL) x (4.184 J/g°C) x (70.0°C - 20.0°C)] water + [(10.0 J/°C) x (70.0°C - 20.0°C)] cup

ie..
Qtotal = 49424 J + 500J = 49924J

and that is per 20.00 seconds... right?
so..
J/s = 49924J / 20.00s = 2471 J/s = 2471 watts = 2.47 kW.. (watt is joules per second !)

*********
questions?