Question

You place a cup of 210oF coffee on a table in a room that is 68oF, and 10 minutes later, it is 200oF. Approximately how long will it be before the coffee is 180oF?

Answer 1

can anyone help me using newton's law of cooling

Answer 2

\[\frac{dT}{dt} = k (T - 68)\]
\[\int\limits \frac{dT}{T - 68} = k \int\limits dt\]
\[\ln (T-68) = kt + C\]
\[T = C e^{kt} + 68\]
Given: t=0, T = 210
t = 10, T = 200

\[\rightarrow C = 142\]
\[\rightarrow k = \frac{1}{10}\ln (\frac{132}{142})\]
Find t when T = 180