Concept explainers
Patients undergo dialysis treatment to remove urea from their blood when their kidneys are not functioning properly. Blood is diverted from the patient through a machine that filters out urea. Under certain conditions, the duration of dialysis required, given that the initial urea concentration is c > I, is given by the equation
Calculate the derivative of t with respect to c and interpret it.
To find: The derivative of t with respect to c with the equation
Answer to Problem 33E
The derivative of t with respect to c is given as
Explanation of Solution
Given:
The given equation is as below.
Calculation:
Use chain rule to differentiate the equation (1).
Assume the variable u as
Use the expression below.
Substitute
Refer equation (1), separate the term
Indicate it as
Differentiate
Assume the variable l as
Use the expression below.
Substitute
Substitute
Write the interpretation based on the result as below.
The rate of reaction will be fast with higher initial concentration value. The time taken for removing the unit concentration of the material will be lesser as the initial concentration increases.
The derivative of t with respect to c is given as
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