We wish to oven-roast a small full chicken for dinner, but we don't know what the cooking time is for a 1.0 kg bird (and I guess that the internet is down or something!) We know that the raw chicken's properties are: density 1150 kg m-, heat capacity 3600 J kg- K-, and thermal conductivity 0.8 W m K-. The chicken is initially at uniform temperature of 10C and we are cooking it in an oven where the air and inner wall temperatures are 190C. The heat transfer coefficient around the chicken is 10 W m- K-. Assume that radiation heat transfer is negligible for now If you are a vegetarian, you can assume that can assume that the chicken is a ball of tofu with identical material properties and initial conditions. a. (8 Pts) Assume that the chicken can be modelled as a sphere and determine the appropriate solution approach to model the transient cooking process. b. (8 Pts) Regardless of your findings in part a, use the lumped capacitance method to predict the time to cook the chicken to reach an internal temperature of 75C. c. (9 Pts) Now, employ the first term approximation to the infinite series solution to determine the required cooking time such that the chicken temperature is 75C throughout. Also, use this solution to predict the temperature at the middle of the chicken at the cooking time predicted in part b.