Answer to Question #101981 in Physics for Madi

Question

A large container which has 258 g of water initially at 23 °C is placed in a microwave oven. The magnetron in the microwave oven can produce 950 W of EM radiation. The microwave is turned on for 2.5 minutes.
a) Assuming that all the microwave energy is absorbed by the water, how much water is left in the container?
b) The OXO 8716900 electric kettle (1500 W) manufacturer’s claim that it can boil up to 1.75 L of water faster than the microwave, safer than the stovetop, and runs off a mains voltage of 120 V. Compare the efficiency of the two approaches.
c) Name the different ways of heat loss in these systems (Microwave & Kettle) during the heating process.

Answer 1

a) From the conservation of energy:

$$Pt=Mc(T_2-T_1)+mL$$

$$(950)(2.5\cdot 60)=(0.258)(4200)(100-23)+(2300000)m$$

$$m=0.0257\ kg=25.7\ g$$

b) Microwave:

$$E_m=\frac{950}{1000}=0.95\frac{kWh}{week}$$

Kettle:

$$E_k=\frac{1500\cdot 0.375}{1000}=0.56\frac{kWh}{week}$$

Kettle is more efficient than the microwave.

c)Those aren't enormous savings, but if you find yourself boiling water a lot (or if you're in an office with a lot of tea drinkers), they can add up. One thing to also consider is that you are more likely to heat the exact amount of water you need in the microwave, whereas you might overfill the electric kettle and negate your savings with a longer time to boil (so just heat what you need!)