Explanation Given: Carbon dioxide concentration of air entering in the room is 0.06 % , Volume of room is 8000 ft 3 , rate of air entering the room is 2000 ft 3 / min and the initial concentration of carbon dioxide in the room is 0.2 % . Calculation: Rate at which carbon dioxide is entering the room is, R i n = 0.06 % ( 2000 ft 3 / min ) = 0.06 100 ( 2000 ft 3 / min ) = 0.06 × 20 ft 3 / min = 1.2 ft 3 / min Rate at which carbon dioxide is going outside the room is, R o u t = A 8000 × 2000 = A 4 (1) Here, amount of carbon dioxide in the air going outside the room is A . Therefore, resulting differential equation for the rate of flow of carbon dioxide is, d A d t = R i n − R o u t (2) Substitute 1.2 for R i n and A 4 for R o u t in the equation (2). d A d t = 1.2 − A 4 d A d t + A 4 = 1.2 (3) Solution of the equation (2) is, A ( I . F ) = ∫ 1.2 ( I . F ) d x (4) Here, integration factor of the differential equation is ( I . F ) . Integration factor of the differential equation is, ( I . F ) = e ∫ 1 4 d t = e t 4 Substitute e t 4 for ( I . F ) in equation (2). A e t 4 = ∫ 1.2 e t 4 d t A e t 4 = 1

6th Edition

ISBN: 9781284105902

Author: Dennis G. Zill

Publisher: Jones & Bartlett Learning

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Chapter 2, Problem 32CR

To determine

The concentration of carbon dioxide in air of room after 10 min.

The steady state concentration of carbon dioxide in air.

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Chapter 2, Problem 31CR

Chapter 2, Problem 33CR

Chapter 2 Solutions

Advanced Engineering Mathematics

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The concentration of carbon dioxide in air of room after 10 min . The steady state concentration of carbon dioxide in air.

Solution Summary: The author explains the steady state concentration of carbon dioxide in air after 10min and the rate of air entering the room.

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The concentration of carbon dioxide in air of room after 10 min.

The steady state concentration of carbon dioxide in air.

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Chapter 2 Solutions

The concentration of carbon dioxide in air of room after 10 min . The steady state concentration of carbon dioxide in air.

Solution Summary: The author explains the steady state concentration of carbon dioxide in air after 10min and the rate of air entering the room.

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The concentration of carbon dioxide in air of room after 10 min. The steady state concentration of carbon dioxide in air.

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Chapter 2 Solutions

The concentration of carbon dioxide in air of room after 10 min.

The steady state concentration of carbon dioxide in air.