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

`(dT)/(dt)=k|T-M|`

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.

`(dT)/(dt)\propto |T-M|`

`\implies (dT)/(dt)=k|T-M|`

Where, k is the constant of proportionality.