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Calculus with Applications | 10th Edition | ISBN: 9780321749000 | Authors: Margaret L. Lial, Raymond N. Greenwell, Nathan P. Ritchey
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Solved: Newton’s Law of Cooling Newton’s law of cooling

Chapter 2, Problem 44A

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QUESTION:

Problem 44A

Newton’s Law of Cooling Newton’s law of cooling says that the rate at which a body cools is proportional to the difference in temperature between the body and an environment into which it is introduced. This leads to an equation where the temperature f(t) of the body at time t after being introduced into an environment having constant temperature T0 is

f(t) = T0 + Ce−kt,

where C and k are constants. Use this result.

If C = 100, k = 0.1, and t is time in minutes, how long will it take a hot cup of coffee to cool to a temperature of 25°C in a room at 20°C?

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QUESTION:

Problem 44A

Newton’s Law of Cooling Newton’s law of cooling says that the rate at which a body cools is proportional to the difference in temperature between the body and an environment into which it is introduced. This leads to an equation where the temperature f(t) of the body at time t after being introduced into an environment having constant temperature T0 is

f(t) = T0 + Ce−kt,

where C and k are constants. Use this result.

If C = 100, k = 0.1, and t is time in minutes, how long will it take a hot cup of coffee to cool to a temperature of 25°C in a room at 20°C?

ANSWER:

Solution

Step 1 of 2

In this problem, we have to find the time to take a hot cup of coffee to cool using newton’s law of cooling.

Given that  

Where  and K are constants.

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