Derive the differential equation relating the chicken’s temperature T(t) and the room temperature.

A chicken is taken out of the oven at a uniform temperature of 150°C and is left out in the open air at the room temperature of 25°C. Assume that the chicken can be approximated as a lumped model. The estimated parameters are mass = 1.75 kg, heat transfer surface area

= 0.3 m2, specific heat capacity = 3220 J/(kg・°C), and heat transfer coefficient

= 15 W/(m2・°C).

a. Derive the differential equation relating the chicken’s temperature T(t) and the room temperature.

b. Using the differential equation obtained in Part (a), construct a Simulink block diagram and find the temperature of the chicken.

c. Build a Simscape model of the system, and find the temperature output of the chicken.

d. Assume that the chicken can be served only if its temperature is higher than 80°C. Based on the simulation results obtained in Parts (b) and (c), can the chicken be left at the room temperature of 25°C for 1 hour?

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