Question

A chef, on finding his stove out of order, decides to boil the water for his wife's coffee by shaking it in a thermos flask. Suppose that he uses tap water at 16°C and that the water falls 27 cm each shake, the chef making 29 shakes each minute. Neglecting any loss of thermal energy by the flask, how long (in minutes) must he shake the flask until the water reaches 100°C? The specific heat of water is 4186 J/kg·K

Answer 1

Heat energy = mass * specific heat * change in temperature

We don't know the mass of the water, so let's call it M kg.
Given specific heat = 4186 J/kg·K
Change in temperature = (100°C - 16°C) = 84°C { = 84K}

So our chef needs to provide an amount of energy (E) where:
E = ( M * 4186 * 84 ) = 351624 * M joules

Now we need the relationship for gravitational potential energy:

g.p.e. = mgh

where m is the mass, g is the acceleration due to gravity and h is the change in height. {I'll assume g = 9.81 m/s²}

Each time the water falls 27 cm {Units Alert! 27 cm = 0.27 m} the lost g.p.e. will be turned into heat energy. Each shake of the M kg of water in the flask will therefore produce:

g.p.e. lost = M * 9.81 * 0.27 = 2.6487 * M joules

So how many shakes will it take to produce 351624 * M joules, if each shake produces 2.6487 * M joules ?

(351624 * M) / (2.6487 * M) = 132753.42 shakes

{notice that the M cancels out}

So if the chef can do 29 shakes per minute, it will take him:

134334 / 33 = 4577.704 minutes