Question

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 0.4. Suppose the ambient temperature TA(t) is equal to a constant 68 degrees Celsius. Write the differential equation that describes the time evolution of the temperature T of the object.

Answer 1

Step-by-step explanation:

Let T be the temperature of an object at time t , then

dT / dt will be rate of change of temperature

According to newton's law of cooling

dT / dt = k ( T - T₂ )

where T₂ is temperature of surrounding , T is temperature of object , k is a constant .

dT / dt = k ( T - T₂ )

Given k = .4 , ambient temperature T₂ = 68⁰C

dT / dt = .4 ( T - 68 )

dT / ( T - 68 ) = .4 dt .

This is required differential equation .