1) Although accuratcly evaluating the cncrsy balance for a person is a complex problem, a simple (but reasonably accurate) model can be devcloped by assurning that the person has a uniform body temperature, that heat transfer to the air is governod by a single heat transfer coefficient, and that metabolism can simply be described in terms of a change in internal energy. Under these conditions, the encrgy balance becomes: mC,dtdT=hA(TTd)+Qmotum where m70kg is the body mass, Cp1kcal/kg/K is the body's heat capacity, and A1.8m2 is the surface area. A) Evaluate the "comfort temperature" for a person, defined as the air temperature at which the body temperature is at steady-state. The heat transfer coefficient for the human body is 4.5kcal/hrm2/K, the body temperature is 37C, and Qaudulim120kcal/hr. B) When you are ill, your body increases Qaudum to help fight off the discase. How long would it take for your body temperature to reach 39if your metabolism were to immediately increase by 20%6 ? Assume that T is equal to the comfort temperature evaluated in A. 2) Consider the energy transfer between a can of soda and the water in a cooler (you can assume that the cooler contains only cold water and no ice). A) Derive an expression for the temperature of the soda and of the water in the cooler as a function of time. Express your results in terms of the volume of the soda, the volume of water in the cooler, the heat transfer cocfficient, and the contact area. B) How long will it take the soda to cool from 20C to 4C if the water is initially at 0C, Vmula0.5L, Veeukr5L, and hA 5kcalhrK ? C) What is the steady-state temperature of the soda and the water in the cooler for the conditions in part B? D) The analysis presented in (A) to (C) ignores the encrgy transfer from the water in the cooler to the surrounding air. Evaluate the steady-state temperature of the soda and water if the heat transfer coefficient for the cooler is h,A81 kcal hr K and T20C