# A hot object introduced to a cold environment will cool at a rate proportional to the excess of...

## Question:

A hot object introduced to a cold environment will cool at a rate proportional to the excess of its temperature above that of its environment. If a cup of coffee sitting in a room at a temperature of 20 {eq}^oC {/eq} cools from 90 {eq}^oC {/eq} to 40 {eq}^oC {/eq} in 10 minutes, how much longer will it take to cool to 30 {eq}^oC {/eq}?

Draw a graph of the temperature ({eq}^oC {/eq}) of the cup of coffee against time (minutes).

## Newton's Cooling Law

When an object is introduced into an environment with different temperature, the temperature of the object will change such the it will be in equilibrium with the surrounding. This change is given by an exponential equation called Newton's cooling law equation.

Newton's cooling law equation is given by

{eq}\displaystyle T(t) = T_s + (T_0-T_s)e^{-kt} {/eq}

where {eq}T(t) = \text{ temperature at time t},...

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