Question

1. One of the realizations of English physicist Sir Isaac Newton was that

The rate of heat loss of a body is proportional to the temperature difference between the body and its surroundings.
or, if T is the temperature of the object, A the temperature of the surroundings, and k the rate of cooling

dT/dt = - k( T - A )

Suppose Anduril has just been reforged from the shards of Narsil and is placed in a basin of water to cool. The initial temperature of the sword is 1300 degrees Fahrenheit and the temperature of the water is 60 degrees Fahrenheit. If the cooling rate of the sword...

Answer 1

....(when placed in water) is k = .368, find how long it takes the sword to cool to 75 degrees.
In particular you should:
_ Solve the differential equation.
_ Solve for the constant of integration using the initial condition.
_ Use the resulting equation to solve for t in terms of T to get the final answer.