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 14°C and that the water falls 34 cm each shake, the chef making 32 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

As we know that -

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 - 14°C) = 86°C { = 86 K}

So our chef needs to provide an amount of energy (E) where:

E = ( M * 4186 * 86 ) = 359996 * M joules

Now we need the relationship for gravitational potential energy:

Gravitational Potential Energy (GPE) = mgh

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

Each time the water falls 34 cm (0.34 m) the lost GPE will be turned into heat energy. Each shake of the M kg of water in the flask will therefore produce:

GPE lost = M * 9.81 * 0.34 = 3.3354 * M joules

So how many shakes will it take to produce 359996 * M joules, if each shake produces 3.3354 * M joules ?

(359996 * M) / (3.3354 * M) = 107932 shakes

So if the chef can do 32 shakes per minute, it will take him:

107932 / 32 = 3373 minutes

Therefore, the chef will require to shake the flask for 3373 minutes to achieve the water temperature upto 100 degC. (Answer)