# Newton's Law of Cooling

A hard-boiled egg is removed from a pot of hot water and set on the table to cool. Let the temperature of the body at time t be T(t). Assume the change of the temperature of the body satisfies Newton's law of cooling: (Please see attachment).

(i) Initially, the egg's temperature is 90 degree C. After an hour its temperature is 60 degree C. Solve the differential equation and hence determine the function T in terms of t.

(ii) When will the egg's temperature be 50 degree C?

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#### Solution Preview

A hard-boiled egg is removed from a pot of hot water and set on the table to cool. Let the temperature of the body at time be Assume the change of the temperature of the body satisfies Newton's law of cooling: where and µ is a constant.

(i) Initially, the egg's temperature is . After an hour its temperature is . Solve the differential equation and hence ...

#### Solution Summary

The expert examines an how the change in temperature of the body satisfies Newton's law of cooling. A step by step solution provided.