Answer Happy

5. The rate of decrease of the temperature of a liquid is proportional to the amount by which this temperature exceeds the temperature of its surroundings. This is known as Newton's law of Cooling. Taking O as the excess temperature at any time t, and 0, as the initial excess, a) show that 0 = 0,e-k. b) A pan of water at 65 °C is standing in a kitchen whose temperature is a steady 15 °C. 1

i) show that, after cooling for t minutes, the water temperature, , can be modelled by the equation $=15+50e-k where k is a constant. ii) Given that after 10 minutes the temperature of the water has fallen to 50 °C, find the value of k. iii) Find the temperature after 15 minutes and sketch the graph relating Ø and t. iv) Do you think that this model would be appropriate for a cooling time of 24 hours?