Question

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

Answer 1

The required equation would be
`(dT)/(dt)=k|M-T|`

Where, k is constant of proportionality.

Explanation:

Differential equation : is an equation that contains one or more functions and their derivatives.

Where, derivatives shows the rate of change of a variable with respect to other variable.

Given,

Change in temperature T of coffee with respect to t ( time ) is proportional to difference between the fixed temperature M and temperature of coffee,

i.e.
`(dT)/(dt)\propto |M - T|` ( if M > T, Change is M - T if M < T then change is T - M)

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

Where,

k = constant of proportionality.