A block of aluminum is heated to a temperature of 100 C. It is then dropped into a flowing stream of water that is held at a constant temperature of 10 C. After 10 seconds, the temperature of the block is 60 C. (Aluminum is such a good heat conductor that its temperature is essentially uniform throughout its volume during the cooling process.) The rate of cooling is proportional to the temperature difference between the block and the water. Write a differential equation for this system with the temperature of the water as the excitation and the temperature of the block as the response.

Determine the equation for the temperature of the block as a function of time. The equation for the temperature of the block as a function of time is (ANS) e-t+(Ans)