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Correct Answer: 1.48 million pounds per hour.
to determine the mass rate of flue gases being exhausted from the coal-fired power plant, we need to apply the principle of conservation of mass. this principle states that the total mass entering a system must equal the total mass exiting the system when the system is at a steady state. we can use this principle to set up an equation accounting for all inputs and outputs of the system.
let's break down the inputs and outputs:
1. **inputs**:
- coal is being burned at a rate of 100 tons per hour. since 1 ton is equal to 2000 pounds, the coal input can be calculated as \(100 \times 2000 = 200,000\) pounds per hour.
- air is flowing into the combustion chamber at a rate of 1.3 million pounds per hour.
2. **outputs**:
- ash is produced at a rate of 10 tons per hour, which equals \(10 \times 2000 = 20,000\) pounds per hour.
- flue gases, which are the main subject of our calculation.
applying the conservation of mass, we set up the following equation:
\[ \text{total input} = \text{total output} \]
\[ \text{coal input} + \text{air input} = \text{flue gas output} + \text{ash output} \]
plugging in the known values:
\[ 200,000 \, \text{lb/hr (coal)} + 1,300,000 \, \text{lb/hr (air)} = \text{flue gas output} + 20,000 \, \text{lb/hr (ash)} \]
to find the flue gas output, rearrange the equation:
\[ \text{flue gas output} = 200,000 + 1,300,000 - 20,000 \]
\[ \text{flue gas output} = 1,480,000 \, \text{lb/hr} \]
therefore, the mass rate of flue gases being exhausted from the plant is 1.48 million pounds per hour. this calculation ensures that the mass balance is maintained as required by the principle of conservation of mass, thereby confirming that the inputs and outputs within the system are equal.
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