Question

Write a differential equation that fits the physical description. The rate of change in the temperature T of coffee at time t is proportional to the difference between the temperature M of the air at time t and the temperature of the coffee at time t.

Answer 1

Answer:

$\frac{dT}{dt}=k|T-M|$

Step-by-step explanation:

Given,

The rate of change in the temperature T of coffee at time t is proportional to the difference between the temperature M of the air at time t and the temperature of the coffee at time t,

i.e.

$\frac{dT}{dt}\propto |T-M|$

$\implies \frac{dT}{dt}=k|T-M|$

Where, k is the constant of proportionality.