10-2. The initial temperature of the hot cof- fee cup shown in Fig. P10.2 is 7(0)...

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10-2. The initial temperature of the hot cof- fee cup shown in Fig. P10.2 is 7(0) = 175°F. The cup is placed in a room tem- perature of T = 70°F. The tempera- ture T(1) of the coffee at time t can be approximated by Newton's law of cool- ing as dT dt +kT(t) = k T (0) where k is a constant. (a) Find the transient solution, Tiran (1). What is the time constant of the response? (b) Find the steady-state solution Tss(1). (c) Determine the total solution T(t). Figure P10.2 A hot coffee cup placed in a room emperature of 70°F. (d) Sketch the total solution T(t). How long does it take for the tem- perature to reach 101% of the room temperature? 10 10-2. The initial temperature of the hot cof- fee cup shown in Fig. P10.2 is 7(0) = 175°F. The cup is placed in a room tem- perature of T = 70°F. The tempera- ture T(1) of the coffee at time t can be approximated by Newton's law of cool- ing as dT dt +kT(t) = k T (0) where k is a constant. (a) Find the transient solution, Tiran (1). What is the time constant of the response? (b) Find the steady-state solution Tss(1). (c) Determine the total solution T(t). Figure P10.2 A hot coffee cup placed in a room emperature of 70°F. (d) Sketch the total solution T(t). How long does it take for the tem- perature to reach 101% of the room temperature? 10

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a Start by solving the given differential equation using the method of variable separation dTdt kTT ... View the full answer