Question

A freshly brewed cup of coffee has temperature 95°C in a 20°C room. When its temperature is 73°C, it is cooling at a rate of 1°C per minute. When does this occur? (Round your answer to two decimal places.) min Need Help? Read

Answer 1

Using newton's law of cooling

Since the room temperature is 20C, hence the value of Ts will be 20 and when t=0, the T(0) is 95, hence the value of C will be 75, so we can write

T(t) = 20 + 75ekt

After some time, the temperature t0 will be dropped to 73C

$kt_0 = ln(\frac{53}{75})$

Also, we know that change in temperature at 73C being -1C

$k = \frac{-1}{75e^{kt_0}}$

$k = \frac{-1}{53}$

$t_0 = -53ln(\frac{53}{73}) = 16.97$

Hence the answer in two decimal places will be 16.97 minutes

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