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 18°C and that the water falls 28 cm each shake, the chef making 26 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

The quantity of heat needed to raise the temperature of water is given by,

Given,

Since the mass is unknown, lets put it as m. Therefore, the quantity of heat required is given by,

The gravitational potential energy is given by,

Given,

h = 28cm = 0.28m

Each time the water falls 0.28 m the loss in gravitational potential energy will be turned into heat energy. Each shake of the m kg of water in the flask will therefore produce,

So one shake produces m2.744J of energy. So the number of shakes required to produce m343252 J of energy is given by,

Given, he performs 26 shakes each minute. Therefore, the total time taken for this 117876.0933 shakes is given by,

which is nearly 75 hours