10-2. The initial temperature of the hot coffee cup shown in Fig. P10.2 is T(0) =...

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10-2. The initial temperature of the hot coffee cup shown in Fig. P10.2 is T(0) = 175 F. The cup is placed in a room temperature of T = 70 F. The temperature T(t) of the coffee at time t can be approximated by Newton's Law of cooling as where k is the effective heat transfer coefficient. dT +kT(t) = k T, dt Figure P10.2 A hot coffee cup placed in a room temperature of 70 F. a. Find the transient solution Ttran(t). What is the time constant of the response? b. Find the steady-state solution Tss(t). c. Determine the total solution T(t). d. Sketch the total solution T(t). How long does it take for the temperature to reach 99% of the room temperature? e. Would increasing the value of k increase or decrease the time when the temperature of coffee reaches the room temp? f. Would a lower or higher value of k be best for a cup of coffee? 10-2. The initial temperature of the hot coffee cup shown in Fig. P10.2 is T(0) = 175 F. The cup is placed in a room temperature of T = 70 F. The temperature T(t) of the coffee at time t can be approximated by Newton's Law of cooling as where k is the effective heat transfer coefficient. dT +kT(t) = k T, dt Figure P10.2 A hot coffee cup placed in a room temperature of 70 F. a. Find the transient solution Ttran(t). What is the time constant of the response? b. Find the steady-state solution Tss(t). c. Determine the total solution T(t). d. Sketch the total solution T(t). How long does it take for the temperature to reach 99% of the room temperature? e. Would increasing the value of k increase or decrease the time when the temperature of coffee reaches the room temp? f. Would a lower or higher value of k be best for a cup of coffee?