Explanation Determine the rate of change of concentration of salt in terms of the difference between salt in and salt out. Given: The outflow of the tank from the previous exercise is directed into a second tank containing V liters of fresh water where it mixes instantaneously and exits at the same rate of 40 L / min . Calculation: If y 2 ( t ) is the amount of salt in the second tank, then y 2 ( t ) = c 2 ( t ) V and y 2 ' ( t ) = c 2 ' ( t ) V The rate of change in the concentration of salt is d y d t = s a l t i n − s a l t o u t = ( 40 ) ( c 1 ) − ( 40 ) ( y 2 V ) = 40 c 1 − 40 y 2 V Using the values y 2 ( t ) = c 2 ( t ) V and y 2 ' ( t ) = c 2 ' ( t ) V , we get c 2 ' ( t ) = 40 V ( c 1 ( t ) − c 2 ( t ) ) = > c 2 ' ( t ) + 40 V c 2 ( t ) = 40 V c 1 ( t ) We know from the previous solution that c 1 ( t ) = 8 e − 2 t / 5 Therefore, the previous equation becomes c 2 ' ( t ) + 40 V c 2 ( t ) = 320 V e − 2 t / 5 . Multiplying by e 40 t / V we get, ( e 40 t / V c 2 ) ' = 320 V e ( 200 − 2 V ) t / 5 V Integrating we get ( e 40 t / V c 2 ) = 320 V 5 V 200 − 2 V e ( 200 − 2 V ) t / 5 V + C = 800 100 − V e ( 200 −...

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Chapter 10, Problem 52CRE

To determine

The salt concentration $c_{2} (t)$ in the second tank as a function of time in the following cases.

(a) $V = 200$ , (b) $V = 300$ .

In each case, determine the maximum concentration.

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Chapter 10, Problem 51CRE

Chapter 11.1, Problem 1PQ

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The salt concentration c 2 ( t ) in the second tank as a function of time in the following cases. (a) V = 200 , (b) V = 300 . In each case, determine the maximum concentration.

Solution Summary: The author calculates the salt concentration c 2 (t) in the second tank as a function of time.

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The salt concentration $c_{2} (t)$ in the second tank as a function of time in the following cases.

(a) $V = 200$ , (b) $V = 300$ .

In each case, determine the maximum concentration.

Want to see the full answer?

Chapter 10 Solutions

The salt concentration c 2 ( t ) in the second tank as a function of time in the following cases. (a) V = 200 , (b) V = 300 . In each case, determine the maximum concentration.

Solution Summary: The author calculates the salt concentration c 2 (t) in the second tank as a function of time.

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The salt concentration c2(t) in the second tank as a function of time in the following cases. (a) V=200, (b) V=300. In each case, determine the maximum concentration.

Want to see the full answer?

Chapter 10 Solutions

The salt concentration $c_{2} (t)$ in the second tank as a function of time in the following cases.

(a) $V = 200$ , (b) $V = 300$ .

In each case, determine the maximum concentration.