Explanation 1) Concept: Form the differential equation from the given information. 2) Given: The air in theroom has volume 180 m 3 with 0.15 % carbon dioxide initially. Fresh air with 0.05 % carbon dioxide flows into the room at the rate 2 m 3 / m i n Calculation: Let y ( t ) be the amount of carbon dioxide in the room after t minutes. y 0 = 0.0015 180 = 0.25 m 3 d y d t = r a t e i n - r a t e o u t R a t e i n = 0.005 2 m 3 m i n = 0.001 m 3 m i n R a t e o u t = y 180 2 m 3 m i n = - y 90 m 3 m i n d y d t = 0.001 - y 90 = 9 - 100 y 9000 m 3 m i n d y d t = 9 - 100 y 9000 d y 9 - 100 y = d t 9000 ∫ d y 9 - 100 y = 1 9000 ∫ d t - 1 100 l n 9 - 100 y = t 9000 + C Since y 0 = 0.27 , we have C = - 1 100 ln ⁡ 18 Substitute C in previous step

8th Edition

ISBN: 9781285740621

Author: James Stewart

Publisher: Cengage Learning

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Chapter 9.3, Problem 46E

To determine

To find:

(a) The percentage of carbon dioxide in a room as a function of time

(b) What happens in the long run.

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Chapter 9.3, Problem 45E

Chapter 9.3, Problem 47E

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( a ) The percentage of carbon dioxide in a room as a function of time ( b ) What happens in the long run.

Solution Summary: The author calculates the differential equation based on the given information. The air in the room has volume 180m3 with 0.15% carbon dioxide initially.

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To find:

(a) The percentage of carbon dioxide in a room as a function of time

(b) What happens in the long run.

Want to see the full answer?

Chapter 9 Solutions

( a ) The percentage of carbon dioxide in a room as a function of time ( b ) What happens in the long run.

Solution Summary: The author calculates the differential equation based on the given information. The air in the room has volume 180m3 with 0.15% carbon dioxide initially.

Concept explainers

Videos

To find: (a) The percentage of carbon dioxide in a room as a function of time (b) What happens in the long run.

Want to see the full answer?

Chapter 9 Solutions

To find:

(a) The percentage of carbon dioxide in a room as a function of time

(b) What happens in the long run.