Question

Estimate how long it should take to bring a cup of water to boiling temperature in a typical 600 -watt microwave oven, assuming that all the energy ends up in the water. (Assume any reasonable initial temperature for the water.) Explain why no heat is involved in this process.

Short answer

Time taken will be approx: 157 sec

Step-by-step solution

Given information

Power P = 600 W

Boiling temp = 100^oC

Explanation

Energy required to raise the temperature of the water is calculated by

$Q=mC\Delta T..................................\left(1\right)$

Where

m= mass of water

C= Specific heat = 4186 J/KgK

ΔT = Change in temp

Power is calculated by

$$\begin{gathered} P=\frac{Q}{t} \\ rearrange \\ t=\frac{Q}{P}.......................................\left(2\right) \end{gathered}$$

From (1) and (2) we can find

$t=\frac{mC∆T}{P}.......................................\left(3\right)$

Substitute values and calculate

Assume water in cup is 250 g = 0.25 kg

$$\begin{gathered} t=\frac{mC∆T}{P}=\frac{(0.25kg)\times (4186J/kgK)\times (90K)}{600W} \\ t=156.975s\approx 157s. \end{gathered}$$

It will take 157 sec.