Newton's Law $of$ Coolin$\frac{g}{W}$arming: According $to$ Newton's empirical law $of$ coolin$\frac{g}{w}$arming, the

rate $at$ which the temperature $of$ a body changes $is$ proportional $to$ the difference between the

temperature $of$ the body and the temperature $of$ the surrounding medium, the $so-$called ambient

temperature. $IfT(t)$ represents the temperature $of$ a body $at$ time $t,T_m$ the temperature $of$

the surrounding medium, and $\frac{dT}{dt}$ the rate $at$ which the temperature $of$ the body changes, then

Newton's law $of$ coolin$\frac{g}{w}$arming translates into the mathematical statement

$\frac{dT}{dt}$propT$-T_m,or,\frac{dT}{dt}=k(T-T_m)$

where $kis$ a constant $of$ proportionality. $In$ either case, cooling $or$ warming, $if{T}_{m}is$ a constant,

$it$ stands $to$ reason that

Exercise$-7$: When a cake $is$ removed from $an$ oven, its temperature $is$ measured $at300F.$ Three

minutes later its temperature $is200F.$ How long will $it$ take for the cake $to$ cool off $to$ a room

temperature $of70F?$

Exercise$-8$: A small metal bar, whose initial temperature was $20C,is$ dropped into a large

container $of$ boiling water. How long will $it$ take the bar $to$ reach $90Cifitis$ known that its

temperature increases $2in1$ second? How long will $it$ take the bar $to$ reach $98C?$