Question

Estimate how long it should take to bring a cup of water to boiling temperature in a typical $600-\mathrm{watt}$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 is taken to boil$2.616$ minutes to raise the $20\mathrm{ml}$water fromlocalid="1648467354265" $10°\mathrm{C}$to$100°\mathrm{C}$.

Step-by-step solution

Step 1. Finding Amount of heat.

Consider a mug filled with$250\mathrm{mL}$cold$10°\mathrm{C}$water in a $600\mathrm{watt}$microwave. To achieve the boiling point, So must raise the temperature by$90˚\mathrm{C}$.

$\mathrm{Q}=\mathrm{mC\Delta T}$

$\mathrm{m}=$Water mass.

$\mathrm{C}=$Specific heat $\mathrm{C}=4.186\mathrm{J}/\mathrm{g}·{}^{\circ }\mathrm{C}$

$\mathrm{\Delta T}=90°$Temp

Therefore,

$\mathrm{Q}=250\times 4.186\times 90=94185\mathrm{J}$.

Step 2. Boiling time.

The Power

$\mathrm{P}=\frac{\mathrm{Q}}{\mathrm{t}}\to \mathrm{t}=\frac{\mathrm{Q}}{\mathrm{P}}$

Insert $\mathrm{Q}$and $\mathrm{P}$values.

$\mathrm{t}=\frac{94185}{600}=156.975\mathrm{s}=2.616\min$.

Normally, heat is transferred from the hotter to the colder object. However, because there is no hot item in our scenario, the heat is transported to the mug via an electromagnetic wave generated by the magnetron.