Time for 212 g of water to boil in a 1219 W microwave

[yaylee]

Homework Statement

A microwave oven produces energy at a rate of P = 1219 W, all in the form of microwaves. When a cup of water is placed into this oven, 64.4% of the microwaves are absorbed by the water. If a cup containing mw = 212 grams of water (227 g equals 8 ounces) starts at temperature Tw = 19.6o C: find t, the time it will take the water to reach its boiling point.

Homework Equations

Q = mcΔT
P = dW/dt

The Attempt at a Solution

Heat needed to raise 0.212 kg of water from 19.6 C to 100 C = (0.212)(4186)(100-19.6)
Q = 71349.53 Joules

Rate of Energy Absorption of Water = (64.4/100)(1219 Joules/sec) = 785 Joules/sec

Since water is absorbing heat at 785 Joules per second, in order to absorb 71349.53 Joules altogether, we need:
t = 785 J/s / 71349.53 J = 0.011 seconds.

Am I approaching the problem incorrectly?

Many thanks in advance!

 

[gneill]

Homework Statement

A microwave oven produces energy at a rate of P = 1219 W, all in the form of microwaves. When a cup of water is placed into this oven, 64.4% of the microwaves are absorbed by the water. If a cup containing mw = 212 grams of water (227 g equals 8 ounces) starts at temperature Tw = 19.6o C: find t, the time it will take the water to reach its boiling point.

Homework Equations

Q = mcΔT
P = dW/dt

The Attempt at a Solution

Heat needed to raise 0.212 kg of water from 19.6 C to 100 C = (0.212)(4186)(100-19.6)
Q = 71349.53 Joules

Rate of Energy Absorption of Water = (64.4/100)(1219 Joules/sec) = 785 Joules/sec

Since water is absorbing heat at 785 Joules per second, in order to absorb 71349.53 Joules altogether, we need:
t = 785 J/s / 71349.53 J = 0.011 seconds.

Am I approaching the problem incorrectly?

Many thanks in advance!

You're doing fine up to the last expression. Check how the units cancel.

Also, does 0.011 seconds seem a reasonable amount of time to heat up that quantity of water in a microwave?

 

[yaylee]

Thanks Gneill!

Also, just curious: do you guys help out students (like myself) voluntarily? If so , that is awfully nice !

 

[gneill]

Thanks Gneill!

Also, just curious: do you guys help out students (like myself) voluntarily? If so , that is awfully nice !

You're welcome. Yes, it's a voluntary activity and we're happy to help!