Heat capacity is the amount of energy you need to add to an object to warm it up by 1K. The heat capacity of water is 4.18 J/g/K; in other words, if you add 4.18 J to 1 g of water, the water will warm by 1K. Imagine you have a cup containing 200 g of water that is absorbing 150W of power. Check your answers by making sure the units work out.

(a) At what rate is the water warming? Answer in kelvin per second.

(b) If the cup starts at room temperature, use the answer to part (a) to estimate how long would you have to heat it to reach boiling.

(c) As the cup heats up, it will radiate more energy to the room. Estimate how much energy the cup is emitting when it reaches the boiling point. You’ll have to estimate some quantities yourself to do this.

(d) Would including enhanced radiation to the room make the water boil faster or will it take longer to boil than was estimated in part (b)?