Microwave energy problem (please check my answers)

[madeeeeee]

Homework Statement

Power microwave problem?
A 1000W microwave oven heats 500 g of water from 10.0 degrees Celsius to 55.0 degrees C in a time of 2 min. the heat capacity of water is 4200 J/kgdegrees C

Homework Equations

have i done this properly? there are 4 other questions with this

The Attempt at a Solution

P=1000W
m=0.5kg
T1=10.0C
T2=55.0C
change in T=45C
t=120s
c=4200J/kg degress C

a) how much thermal energy did the water gain?

have i done this correctly

Q=mcT
=(.5kg)(4200 J/kgC)(45C)
=94500 J
Q=9.5 x 10^4 J

b)How much power was associated with this thermal energy?

have i done this correctly

P=E/t
=9.5x10^4 J / (120s)
P=787.5 W

c) What percentage of the electricity power that went into the microwave actually went into heating the water?

Did i do this correctly

787.5 W / 1000 W x 100
= 79%

d) Why didn't all the electricity energy of the microwave get converted to thermal energy of the water?

Because loss of energy was also due to opperating the microwave and making cup of water spin

What are other reasons?

Thanks!

 

[sylas]

It all looks about right to me. There's a bit of energy going into the heating the air and the cup, but I that would be small. The spinning of the cup would be even smaller. Mostly losses of some kind in the microwave operation sounds about right to me. A microwave oven usually has vents around the back to help get rid of waste heat, which would be most of the losses.

Cheers -- sylas

 

[kerimek]

Yes, your calculations for parts a, b, and c seem correct. As for part d, there are a few other reasons why not all of the electricity energy gets converted to thermal energy in the water. One is the inefficiency of the microwave itself, which means that not all of the electricity is actually used to generate microwave energy. Another reason is that some of the energy is lost as heat to the surrounding air or through the walls of the microwave. Additionally, some of the energy may be used to power the rotating plate or other features of the microwave. Overall, there are always some losses when converting one form of energy to another, so it is normal for not all of the electricity energy to be converted to thermal energy in the water.