A chicken is taken out of the oven at a uniform temperature of \(150^{\circ} \mathrm{C}\) and is left out in the open air at the room temperature of \(25^{\circ} \mathrm{C}\). Assume that the chicken can be approximated as a lumped model. The estimated parameters are mass \(m=1.75 \mathrm{~kg}\), heat transfer surface area \(A=0.3 \mathrm{~m}^{2}\), specific heat capacity \(c=3220 \mathrm{~J} /\left(\mathrm{kg} \cdot{ }^{\circ} \mathrm{C}\right)\), and heat transfer coefficient \(h=15 \mathrm{~W} /\left(\mathrm{m}^{2 \cdot}{ }^{\circ} \mathrm{C}\right)\).

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 \(80^{\circ} \mathrm{C}\). Based on the simulation results obtained in Parts (b) and (c), can the chicken be left at the room temperature of \(25^{\circ} \mathrm{C}\) for 1 hour?