Explanation Given: The addition of smoke is 5 ppm . Approach: Use the concept of separable differential equation. An equation is separable if it can be written in the form ∫ q ( y ) d y = ∫ p ( x ) d x Calculation: Use the fact that the change in smoke will be the rate of smoke in, that is ( d y d t ) in minus the rate of smoke out ( d y d t ) out as follows, d y d t = ( d y d t ) in − ( d y d t ) out … ( 1 ) Here, the rate of smoke into the room is 5 ppm . Therefore, ( d y d t ) in = 5 ppm While the rate out will be the current amount of smoke, y divided by the air times the rate or as follows, ( d y d t ) out = ( y V ) d V d t The equation (1) will become as follows, d y d t = 5 − ( y V ) d V d t … ( 2 ) Substitute 15000 for V and 1200 for d V d t in equation (2). d y = 5 − ( − y 15000 ) ( 1200 d t ) = 5 − ( 2 y 25 ) = 125 − 2 y 25 Use the concept of separable differential equation.

2nd Edition

ISBN: 9780321964038

Author: GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher: Pearson Addison Wesley,

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Chapter 11.CR, Problem 61CR

To determine

To find:

The time required to reduce the smoke content to 10 ppm.

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