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

Answer:

$\frac{dQ}{dt} =-hA\Delta T(t)$

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,

$\frac{dQ}{dt} =-hA [T(t)-T(s)]$

$\frac{dQ}{dt} =-hA\Delta T(t)$

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