Question

A body cools at the rate of ${1.2}^{0}C$ per minute when its temperature is more that of the surroundings by ${40}^{0}C$. Find the rate of cooling of the body when its temperature is more than that of surroundings by ${25}^{0}C$.

Answer 1

Rate of cooling $\frac{dT}{dt}=-\frac{k}{ms}(T-T_s)$

Or $1.2=\frac{-k}{ms}\left(40\right)$ .......(1)

Or $\frac{dT}{dt}=\frac{-k}{ms}\left(25\right)$ ......(2)

So, $\frac{dT/dt}{1.2}=\frac{25}{40}$

$⟹\frac{dT}{dt}=0.75{}^{o}C$ per minute