Question 3 A heater is used to increase the concentration of

Question 3

A heater is used to increase the concentration of sugar in maple syrup. At the beginning there were 500 lbs of syrup in the heater and the mass fraction of the sugar (C₁₂H₁₂O₁₁) in the Syrup was 0.01. The flow rate of the water exiting is 25 lbs/h. Write the differential equation expressing the transition region. How long (in hours) will it take for the mass fraction to reach a value of 0.1.

Solution

Given,

Initial Total Mass = Mass of sugar initial + Mass of water initial

                                 = M_s1 + M_w1 = 500 lbs

Since,

M_s1 / (M_s1 + M_w1 ) = 0.01

99*M_s1 = M_w1

M_s1 = 5 lbs

M_w1 = 495 lbs

Since, final desire mass ratio is 0.1

M_s2 / ( M_s2 + M_w2 ) = 0.1

Here, M_s1 = M_s2

M_w2 = 45 lbs

Let time required for change of mass ratio is T

( M_w2 – M_w1 ) = rate of water exit * T = 25 * T

T = 18 hour