Cooking a Thanksgiving turkey is an art form and, if your skills in the kitchen are like mine, it is sometimes more of a mystical., elusive art form. Thankfully, science also has much to contribute in the kitchen as well as the laboratory. Let us consider the change in temperature of a common, 20-lb holiday fowl as it is cooked in a convection oven. To simplify the analysis, let's assume the bird can be modeled as a uniform sphere of radius 7.0 in. with a specific heat of 3.53 kJ/kg-K. Moreover, the turkey will be assumed to have a uniform temperature,

T: throughout that will change with time as it is cooked according to the following relationship: T(t) = T_infinity - (T_0 - T_integral) e^-ha_s/pcp^v where To is the initial temperature of the turkey, T_infinity, is the oven temperature, V is the volume of the turkey, As is the surface area of the turkey, and h is the convection coefficient for the scenario which is 11.3 W/m^2-K. If the oven is set to 325 degree F and the initial temperature of the turkey is 50 degree F, calculate how much time it takes for the turkey to reach 170 degree F.