Question

A thermometer reading 100◦F is placed in a medium having a constant temperature of 70◦F. After 6 min, the thermometer reads 80◦F.
What is the reading after 20 min?

Answer 1

Answer:

70.00143

Step-by-step explanation:

Given that a thermometer reading 100◦F is placed in a medium having a constant temperature of 70◦F. After 6 min, the thermometer reads 80◦F.

We know that Newton law of cooling has formula as

$T(t) = Ts +(T_0 - T_s)e^{-kt.}$

where Ts is room temperature and To is initial temperature.

Using the fact that when t =6, T (6) = 80

T0 = 100 and Ts =70 we can find k

$80 = 70+(100-70)e^{-6k} \\e^{-6k}=0.33333\\k = 0.1831$

Using this we find temperature when t=20

$T(20) = 70+(100-70)e^{-20*0.1831}\\T(20) = 70+(100-70)e^{-3.6624}\\\\T(20) = 70.00143$