6. (20) The temperature of a turkey in an oven is assumed to be uniform throughout the bird, and neglecting the heat absorbed by the cooking reactions, is given by the following differential equations: MCdT/dt=A[Tov4T4] where M is mass of the turkey, C is its specific heat, is the Stephan-Boltzmann constant equal to 5.67108W/m2K, is the emissivity of turkey skin equal to 0.65,A is the surface area of turkey, T is the temperature of the turkey in K and Tov is the oven temperature in K. (a) Make a linear approximation to the differential equation and obtain the transfer function G(s)=T(s)/T ov (s) (b) For M=10kg,C=2.85kJ/kgK,A=0.3m2, calculate the steady state gain and the time constant of the transfer function. (c) The 10kg turkey is placed in the oven, and initially both the oven temperature and the turkey temperature are uniform at 300K. At t=0, the oven temperature is increased to 400 K. Use your linearized model to calculate the time required for the turkey temperature to reach 350K. (Turkey is considered cooked when its internal temperature reaches 350K.) (d) Repeat part (c), but this time use the exact differential equation without linearization. Based on the answers for parts (c) and (d), comment on the accuracy of the linear approximation