Subtopic: Material and energy balances in food processing systems
Question Statement:
In the production of butter from cream containing $40\%$ fat, the resulting butter contains $80\%$ fat and buttermilk contains $0.5\%$ fat. For $500\text{ kg}$ of cream churned, calculate the mass of butter obtained in $\text{kg}$.
Answer Key:
248.43
Step-by-Step Solution & Explanation
Overall mass balance: $C = B + BM \implies BM = 500 - B$.
Fat balance:
$500 \times 0.40 = B \times 0.80 + (500 - B) \times 0.005$
$200 = 0.80 B + 2.5 - 0.005 B$
$197.5 = 0.795 B$
$B = \frac{197.5}{0.795} \approx 248.428\text{ kg}$