Question

A thermometer is removed from a room where the temperature is 70° F and is taken outside, where the air temperature is 40° F. After one-half minute the thermometer reads 60° F. What is the reading of the thermometer at t = 1 min? (Round your answer to two decimal places.)

Answer 1

Answer:

53.3324

Step-by-step explanation:

given that a  thermometer is removed from a room where the temperature is 70° F and is taken outside, where the air temperature is 40° F.

By Newton law of cooling we have

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

where T (t) is temperature at time t,T =surrounding temperature = 40, T0 =70 = initial temperature

After half minute thermometer reads 60° F. Using this we can find k

$T(0,5) = 40+(70-40)e^{-k/2} = 60\\e^{-k/2} =2/3\\-k/2 = -0.4055\\k = 0.8110$

So equation is

$T(t) = 40+(30)e^{-0.8110t}$

When t=1,

we get

$T(1) = 40+(30)e^{-0.8110}\\\\=53.3324$