Strawberries contain about 15 wt% solids and 85 wt% water. To make strawberry jam, crushed strawberries and sugar are mixed in a 45:55 mass ratio, and the mixture is heated to evaporate water until the residue contains one-third water by mass. (a) Draw and label a flowchart of this process. (b) Do the degree-of-freedom analysis and show that the system has zero degrees of freedom (i.e., the number of unknown process variables equals the number of equations relating them). If you have too many unknowns, think about what you might have forgotten to do. (c) Calculate how many pounds of strawberries are needed to make a pound of jam.

Problem 4.9

Strawberries contain about 15 wt% solids and 85 wt% water. To make strawberry jam, crushed strawberries and sugar are mixed in a 45:55 mass ratio, and the mixture is heated to evaporate water until the residue contains one-third water by mass. (a) Draw and label a flowchart of this process. (b) Do the degree-of-freedom analysis and show that the system has zero degrees of freedom (i.e., the number of unknown process variables equals the number of equations relating them). If you have too many unknowns, think about what you might have forgotten to do. (c) Calculate how many pounds of strawberries are needed to make a pound of jam.

Step by step solution

Step 1 of 3

a)

The flow of the given process as follows.

Here the mass fraction of solids (assume as sugar) in strawberries (of mass m.) is 0.15 and

the mass fraction of water in strawberries is 0.85.

And the mass fraction of sugar in strawberry jam (of mass 1.00 lb) is 0.667 and mass fraction of water in strawberries is 0.33.

____________________________________________________________________________

Step 2 of 3

b)

The number of degrees of freedom is given by equation:

Here, unknowns are mass of strawberries ( m ), sugar (m,) and evaporated water (m.) that is

3. And mass balances for components sugar and water each can be written. Other equation

comes from the mass ratio of sugar to strawberry (which is known).

So, the number of degrees of freedom is

= 3-(2+1)

=10

Therefore, the number of degrees of freedom is 10.

_____________________________________________________________________________

Step 3 of 3

c)

The mass ratio of strawberries to sugar in the initial mixture is 45:55. That is,

Now, write the sugar mass balance equation.

Substitute in above relation and solve form,

Thus, strawberries are needed to make jam.

__________________________________________________________________________