A simplified representation of the temperature dynamics of
Chapter , Problem 7.55(choose chapter or problem)
A simplified representation of the temperature dynamics of two adjacent masses is shown in Figure P7.55. The mass with capacitance \(C_{2}\) is perfectly insulated on all sides except one, which has a convective resistance \(R_{2}\). The thermal capacitances of the masses are \(C_{1}\) and \(C_{2}\), and their representative uniform temperatures are \(T_{1}\) and \(T_{2}\). The thermal capacitance of the surroundings is very large and the temperature is \(T_{o}\).
(a) Develop a model of the behavior of \(T_{1}\) and \(T_{2}\).
(b) Discuss what happens if the thermal capacitance \(C_{2}\) is very small.
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