Question

An object with initial temperature 120° F is submerged in large tank of water whose temperature is

70°F. Find a formula for F(t), the temperature of the object after t minutes, if the cooling constant is

k= 0.2

F(t)=

Answer 1

`F(t)=Ts+(T0-Ts)^{e-0.2t`

Explanation:

Newton's law of cooling states

"that the temperature of a body changes at a rate proportional to the difference in temperature between the body and its surroundings"

Newton's Law of Cooling is given by the formula

`F(t)=Ts+(T0-Ts)^{e-kt`

Where

F( t ) is the temperature of the object at a given time t

T s is the surrounding temperature

T 0 is the initial temperature of the object

k is the constant

Given k=0.2

Hence the expression is

`F(t)=Ts+(T0-Ts)^{e-0.2t`