10) Newton's law of cooling states the the rate of decrease of the temperature of a body is proportional to the amount by which its temperature exceeds the temperature of

its surroundings. If To is the initial temperature of a body, T, is the temperature of its surroundings, and T is the temperature of the body at time t: (a) Form a differential equation for Newton's Law of cooling. (b) By solving your equation, show that T- T, = (To - T,) e-kt, where k is a constant, and state the units of the constant k. (c) Glycerol is to be added to a protein sample prior to storage. The glycerol is heated to 70°C to aid accurate pipetting. To avoid denaturation of the sample, the glycerol must then be allowed to cool to below 27° before being added to the protein. If the ambient temperature is 21° C, the glycerol cools to T = 58°C by time t = 2 minutes. At what time can the glycerol be added to the protein? (d) Using a choice of axes that will allow you easily to predict the temperature of the glycerol, sketch a graph of the anticipated variation of the glycerol temperature with time. (e) Once the glycerol has been added to the protein, will the rate of cooling described by the same constant k? Give reasons for your answer.