Question

When a coil of steel is removed from an annealing furnace its temperature is 684C. Four minutes later its temperature is 246C. How long will it take to reach 100C? Assume that Newton's law of cooling holds, which states that the time rate of change of temperature of a cooling body is proportional to the difference between the temperature of the body and the temperature of the surrounding medium. Assume that room temperature is 27C.

Note: The problem can be solved efficiently by formulating it more generally, as follows. Let T_A be the temperature of the surrounding medium (called the ambient temperature). Let T0 be the temperature of the coil when it is removed from the furnace at time t = 0. The temperature is measured to be T1 at time t1. The problem is to nd the time t2 at which the temperature is T2. So the given quantities are TA; T0; T1; T2 and t1 and the unknown is t2. The idea is to solve the DE for the temperature function T(t) and show that

То-Т T,-T,

Answer 1

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D. t1 0