Chapter 12.5, Problem 57E

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11th Edition

Ronald J. Harshbarger + 1 other

ISBN: 9781305108042

Textbook Problem

** Newton's law of cooling** Newton’s law of cooling (and warming) states that the rate of change of temperature

Suppose an object at

To determine

**To calculate:** The time require by the object to reach the temperature of *T* is the temperature of the surroundings.

Explanation

**Given information:**

The rate of cooling of the object by Newton’s law of cooling is given as, *T* is the temperature of the surroundings. The room temperature is

**Formula used:**

The Newton’s law of cooling is given as,

Where *T* is the temperature of the surroundings *u* is the initial temperature, *t* is any instantaneous time.

The logarithmic rule of integrals,

The natural logarithm property,

**Calculation:**

Consider the rate of cooling of the object,

Rewrite the provided differential equation,

Integrate both side of the equation as:

Now, use the logarithmic rule of integrals to get,

Solve further,

Now, initial temperature of the object is

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