You and another person go to the museum and decide to take a look at an exhibit that has a bike with an attached heating coil/generator. The coil is placed in a tank of water at 20 deg C. Peddling makes the coil increase the energy of the water. The goal is to make the water boil. One of you decides to peddle the bike and raise the temperature to the point of boiling, and the other will make the water boil and keep it at that state. You want to use the least amount of energy; decide whether you want to peddle and raise the temperature or peddle and make the water boil.

Question

It takes 80 calories/gram to raise the temp to boiling point. The latent heat of vaporization is 540 calories/gram, so I thought the first one was easier. However, does it take just 80 cal/gram, or 80 cal/gram per degree (6400 calories)?

Answer 1

The first option:

1 calorie raises the temperature of one gram of water by 1°C.
So 80 cal raises the temperature of 1 g of water by 80 degrees.
(80°=100°-20°)
So it takes 80x cal.to raise the temperature of water to the boiling, where x is the mass of water in the tank.
There is no indication of what x might be, and no indication of what heat loss might be.

2. to keep the water boiling, assuming ZERO heat loss, then you don't need to peddle to keep it at 100°C. ANY peddling will keep the steam coming out.
There is no indication of what heat loss might be.

Sorry, but there is no sensible comparison possible if we do not know the amount of water in the tank, and what the rate of heat loss when water in the tank is at 100°C.

Answer 2

For part two, I think they are referring to the energy it takes to convert liquid water from 100 degrees to boiling water at 100 degrees (latent heat). I understand the first part now.

Answer 3

If it means to boil dry the water in the tank, then it takes 540x calories to boil it dry, compared with 80x to raise the water to 100°C.

However, question says:
"will make the water boil and keep it at that state"
and does not say the tank must be boiled dry!