Newton’s Law of Cooling. According to Newton’s law of cooling, if an object at temperature T is immersed in a medium having the constant temperature M, then the rate of change of T is proportional to the difference of temperature M - T. This gives the differential equation
dT / dt = k(M – T) .
(a) Solve the differential equation for T. (b) A thermometer reading 1000F is placed in a medium having a constant temperature of 700F. After 6 min, the thermometer reads 800F. What is the reading after 20 min? (Further applications of Newton’s law of cooling appear in Section 3.3.)
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