Cooking an apple pie, [25 pts] Consider cooking a 3 pound apple pie from room temperature in a convection oven at 400F. You can assume that the pie is 50% apples, 10% sugar, 10% butter, 5% eggs, and 25% crust/flour (by mass). You cook the pie for X minutes. You can can assume the pie is a cylinder with a height of 2 inches. You can also assume that the heat transfer coefficient between the pie and oven is h=80W/m2/K, such that the rate of heat transfer from the oven to the pie follows: Qin(t)=Apieh[TovenTpie(t)] where Apie is the surface area of the pie and both Qin(t) and Tpie(t) are functions of time. a) Sketch a detailed schematic of this cooking process (including the initial and final states and the corresponding system, boundary, and surrounding conditions). [5pts] b) Sketch (in the left figure) the temperature of the Pie as a function of time. Assume that the Pie doesn't change the temperature of the oven and make sure you annotate the plot axes and different cooking regimes. [ [5pts] c) What is the corresponding energy balance for this Pie cooking problem? [10pts] d) What is the corresponding entropy balance for this Pie cooking problem? 10pts e) What is the mass of each ingredient in the pie? [1 pt/ each] mapples=meggs=mbutter=gggmsugar=mflour=gg f) What are the maximum and minimum rates of heat transfer during the cooking process? (make sure you justify your assumptions) QmaxQmin==[WW[5pts][5pts] g) Calculate the ideal time ( X minutes) for cooking the Pie. For ideal cooking you want the pie to reach 175F and then cook for an additional time to break down the ingredients. For example, say you want to break down (decompose) both the apples and sugar by 50%. You can assume a latent heat for break down (decomposition) for the apples and the sugar of a value that is 1/3 their corresponding latent heat of fusion values. You can neglect boundary work and assume that the temperature of the oven and the mass of the Pie are constants. [20pts] h) Calculate the entropy generated. Assume that the temperature of the oven and the mass of the Pie are constants. Also, when calculating upie and spie make sure you use the mass averaged specific heat and mass averaged specific entropy. For example, the mass averaged latent heat follows as: =mpie1imiLfi where the subscript i represents each corresponding pie ingredient. You will need to calculate these values from tabulated values of food ingredients. Make sure you show your work for partial credit. Answer: kJ/K[10pts]