Question

Material Balance Using Pearson Square

Answer 1

Answer:

1. To produce 5000 quarts of this blended wine you need 1250 quarts of Wine A and 3750 quarts of Wine B.

2. To produce a 500 kg batch, you need  83.8 pounds of cream and 1018.5 pounds of skim milk.

Explanation:

(a) Step 1. Draw the Pearson Square. The opposite corner is the substraction of the large value and the smaller value. For example, the upper-right corner is (12-11) = 1. The Lower right corner is (15-12)=3.

Wine A 15%                            1 parts

                               12%

Wine B 11%                             3 parts

Step 2. The total amount of "parts"is 1+3=4, which 1 part corresponds to Wine A and 3 parts to Wine B.

So, the blend has to be 1/4=0.25 parts of Wine A and 3/4=0.75 parts of Wine B.

We can verify the result

$Alcohol_{blend}=0.25*Alcohol_{A}+0.75*Alcohol_{B)\\Alcohol_{blend}=0.25*0.15+0.75*0.11 = 0.0375+0.0825=0.12$

To produce 5000 quarts of this blended wine you need 1250 quarts of Wine A and 3750 quarts of Wine B.

(b) Step 1. Draw the Pearson square

Cream 40%                                3 parts                    

                               3.5%

Skim milk 0.5%                           36.5 parts

% of Cream = 3/(3+36.5) = 0.076 = 7.6%

% of Skim milk = 36.5/(3+36.5) = 0.924 = 92.4%

$Fat_{StandardMilk} = 0.076*Fat_{cream}+0.924*Fat_{skimmilk}\\Fat_{StandardMilk} = 0.076*40+0.924*0.5= 3.04 + 0.46 = 3.5$

To produce a 500 kg batch, you need 500*0.076= 38 kgs of cream and 500*0.924= 462 kgs of skim milk. This is equivalent to 83.8 pounds of cream and 1018.5 pounds of skim milk (1 kg = 2.2 pounds).