Question

Newton's Law of Cooling says that the rate of cooling of an object is proportional to the difference between its own temperature and the temperature of its surrounding. Write a differential equation that expresses Newton's Law of Cooling for this particular situation.

Answer 1

`(dQ)/(dt) =-hA\Delta T(t)`

Step-by-step explanation:Newton.s law of cooling states that the rate of cooling of an object is proportional to the difference between its own temperatures and temperature of its surroundings. Mathematically,

`(dQ)/(dt) =-hA [T(t)-T(s)]\\`

`(dQ)/(dt) =-hA\Delta T(t)`

where
`Q` is the heat transfer

`h` is heat transfer coefficient

`A` is the heat transfer surface area

`T` is the temperature of the object's surface

`T(s)` is the temperature of the surroundings