The differential equation dT dt = k1[T Tm(t)] + A0, (1.6.13) where k1 and A0 are

Chapter 1, Problem 28

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The differential equation dT dt = k1[T Tm(t)] + A0, (1.6.13) where k1 and A0 are positive constants, can be used to model the temperature variation T (t) in a building. In this equation, the first term on the right-hand side gives the contribution due to the variation in the outside temperature, and the second term on the right-hand side gives the contribution due to the heating effect from internal sources such as machinery, lighting, people, etc. Consider the case when Tm(t) = A B cos t, = /12, (1.6.14) where A and B are constants, and t is measured in hours. (a) Make a sketch of Tm(t). Taking t = 0 to correspond to midnight, describe the variation of the external temperature over a 24-hour period.(b) With Tm given in (1.6.14), solve (1.6.13) subjectto the initial condition T (0) = T0.