Newton's law of cooling states that the temperature of an object changes at a rate proportional to the difference between its temperature and that of its surroundings. If we measure temperature in degrees Celsius and time in minutes, the constant of proportionality k equals 0.3. Suppose the ambient temperature TA(t) is equal to a constant 70 degrees Celsius. Write the differential equation that describes the time evolution of the temperature T of the object.
a. dT/dt =
b. Suppose the ambient temp TA(t) = 66cos((?/30)t) degrees Celsius (time measured in minutes). Write the DE that describes the time evolution of temperature T of the object.
dT/dt =
c. If we measure time in hours the differential equation in part (b) changes. What is the new differential equation?
dT/dt =
d. If we measure time in hours and we also measure temperature in degrees Fahrenheit, the differential equation in part (c) changes even more. What is the new differential equation?
dT/dt =
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