Question

The specific heat of water is 4190 j/(kg*k). suppose you put 1 kg of water (a bit over 4 cups) into a microwave that can deliver 1000 w of power to the water when it is running at full power. roughly how long will you need to run the microwave at full power in order to raise the temperature of the water by 10°c?

Answer 1

Given:
P = 1000 W, power input
c = 4190 J/(kg-K), the specific heat of water
m = 1 kg, mass of water
ΔT = 10 °C = 10 K, temperature rise.

Let t = time required to raise the temperature f the water.
Then
P*t = m*c*ΔT
(1000 J/s)*(t s) = (1 kg)*(4190 J/(kg-K)*(10 K)
1000t = 41900
t = 41.9 s

Answer: 41.9 s or 42 s (approximately)