Grinding very large limestone down to 100 μm requires 12.7 kWh/ton. Using Bond's law, estimate the energy needed to grind from very large feed to 50 μm________________?
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Answer: C. 18 kWh/ton
Explanation
Bond third theory states that work input is inversely proportional to the square root of product size. Halving the product size from 100 micrometers down to 50 micrometers increases energy requirements. Multiplying the initial 12.7 kWh/ton by the square root of two yields approximately 18 kWh/ton. Bond's law is a widely accepted empirical formula used to calculate comminution energy requirements. The work index parameter characterizes the resistance of a given material to crushing and grinding. Energy calculations help engineers select properly sized motors for industrial milling circuits.
Mining operations use Bond's equation to estimate power consumption and operational costs for new mills. Accurate energy estimation prevents undersized motor installations in commercial mineral processing plants. Fine grinding requires disproportionately more energy than coarse crushing due to surface area scaling. Option A represents a halved energy value, which contradicts the fundamental laws of comminution. Option B underestimates the required energy increase dictated by the square root size ratio. Option D overestimates the energy calculation beyond the correct Bond's law mathematical scaling.
- Subject
- Engineering
- Category
- Chemical Engineering
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- medium
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