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Calorimetry

A body cools ...

Question

A body cools at the rate of ${0.5}^{o}$ C $/$ minute when it is $25^{o}$ C above the surroundings. Calculate the rate of cooling when it is $15^{o}$ C above the same surroundings.

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Solution

Rate of cooling is directly proportional to the temperature difference between the body and the surroundings. For temperature difference of $25^{0} C$ , the rate is ${0.5}^{0} C / m i n$ , let for $15^{0} C$ the rate be $x^{0} C / m i n$ . Since they are directly proportional we can write,
$\frac{0.5}{x} = \frac{25}{15}$
$x = \frac{0.5 \times 15}{25} = {0.3}^{0} C / m i n$

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