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Problem: A tank contains 20 kg of salt dissolved in 5000 L of water. Brine that contains 0.03 kg of salt per liter of water enters the tank at a rate of 25 L/min. The solution is kept thoroughly mixed. If the rate of outflow is 30 L/min, what is the concentration of the well-mixed solution after 5 hours have elapsed? Do not round-off intermediate values. Use five decimal places for the final answer. A) 0.03395 kg/L B) 0.00489 kg/L C) 0.19203 kg/L D 0.02000 kg/L E) There is no correct answer from the given options.

Problem: A tank contains 20 kg of salt dissolved in 5000 L of water. Brine that contains 0.03 kg of salt per liter of water enters the tank at a rate of 25 L/min. The solution is kept thoroughly mixed. If the rate of outflow is 30 L/min, what is the concentration of the well-mixed solution after 5 hours have elapsed? Do not round-off intermediate values. Use five decimal places for the final answer. A) 0.03395 kg/L B) 0.00489 kg/L C) 0.19203 kg/L D 0.02000 kg/L E) There is no correct answer from the given options.

College Algebra
College Algebra
1st Edition
ISBN:9781938168383
Author:Jay Abramson
Publisher:Jay Abramson
Chapter6: Exponential And Logarithmic Functions
Section6.1: Exponential Functions
Problem 60SE: The formula for the amount A in an investmentaccount with a nominal interest rate r at any timet is...
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Problem: A tank contains 20 kg of salt dissolved in 5000 L of water. Brine that contains 0.03 kg of salt per liter of water enters the tank at a rate of 25 L/min. The solution is kept thoroughly mixed. If the rate of outflow is 30 L/min, what is the concentration of the well-mixed solution after 5 hours have elapsed? Do not round-off intermediate values. Use five decimal places for the final answer. (A) 0.03395 kg/L (B) 0.00489 kg/L (C) 0.19203 kg/L (D) 0.02000 kg/L (E) There is no correct answer from the given options.
Transcribed Image Text:Problem: A tank contains 20 kg of salt dissolved in 5000 L of water. Brine that contains 0.03 kg of salt per liter of water enters the tank at a rate of 25 L/min. The solution is kept thoroughly mixed. If the rate of outflow is 30 L/min, what is the concentration of the well-mixed solution after 5 hours have elapsed? Do not round-off intermediate values. Use five decimal places for the final answer. (A) 0.03395 kg/L (B) 0.00489 kg/L (C) 0.19203 kg/L (D) 0.02000 kg/L (E) There is no correct answer from the given options.
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From this solution, in the end part why is it 0.15? isn't it supposed to be 0.75? 

Here the given model is f = be Vot(e-f)t dQ dt dQ dt dQ dt + + + 30 I.F⋅ = 5000+(25-30)t 6 1000 -t Q (1000-+)6 11 M 11 Step 2 Now solution is y(IF) = jQ(IF) dx espax es(+) 26in (1000-t) dt (1000-+)6 (1000-1) = √ 00355+6² = Q(0) = 20 20 (10)¹8 dt 0.75 (5) (1000 +)5 +C 0.75 (5) (lay's 0.15 10's = C (0.03) 25 +C 0.75 C =-0-13 x 1015 C =-1-3x10-16 0.02 10/5 Q = (1000+)(0.75) -1-3x10¹6 (1000-ta
Transcribed Image Text:Here the given model is f = be Vot(e-f)t dQ dt dQ dt dQ dt + + + 30 I.F⋅ = 5000+(25-30)t 6 1000 -t Q (1000-+)6 11 M 11 Step 2 Now solution is y(IF) = jQ(IF) dx espax es(+) 26in (1000-t) dt (1000-+)6 (1000-1) = √ 00355+6² = Q(0) = 20 20 (10)¹8 dt 0.75 (5) (1000 +)5 +C 0.75 (5) (lay's 0.15 10's = C (0.03) 25 +C 0.75 C =-0-13 x 1015 C =-1-3x10-16 0.02 10/5 Q = (1000+)(0.75) -1-3x10¹6 (1000-ta
Here 5 hours = SO Q2 (1000-300)6 Q Volume = 300 min 0-15 (1000-300) = 105-15-29437 = 89.70 563 kg (700) (0.15)- (700) x1-3x1016 10 5 (152943-7) 10¹² x10¹6 - 1-3x10-16 = $500 so Concentration = 5000+ (30+25) (300) 89.70563 3500 = 0.02563 kg/L Answer: Ⓒ
Transcribed Image Text:Here 5 hours = SO Q2 (1000-300)6 Q Volume = 300 min 0-15 (1000-300) = 105-15-29437 = 89.70 563 kg (700) (0.15)- (700) x1-3x1016 10 5 (152943-7) 10¹² x10¹6 - 1-3x10-16 = $500 so Concentration = 5000+ (30+25) (300) 89.70563 3500 = 0.02563 kg/L Answer: Ⓒ
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If this is the given model. How to solve this problem? 

Definition of variables: CSTR Model Q(t) = the amount of the quantity of salt dissolved in the well-mixed solution at time t (in minutes). V= the initial volume a = the amount of dissolved substance at time t b= the concentration of the solution being poured in e = inflow f = outflow Model: dQ dt f V₂+ (e-f)t + ( Q = be where Q (0) = a
Transcribed Image Text:Definition of variables: CSTR Model Q(t) = the amount of the quantity of salt dissolved in the well-mixed solution at time t (in minutes). V= the initial volume a = the amount of dissolved substance at time t b= the concentration of the solution being poured in e = inflow f = outflow Model: dQ dt f V₂+ (e-f)t + ( Q = be where Q (0) = a
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