A 75 -hp compressor in a facility that operates at full load for 2500 h a year is powered by an

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A 75 -hp compressor in a facility that operates at full load...

A 75 -hp compressor in a facility that operates at full load for $2500 \mathrm{h}$ a year is powered by an electric motor that has an efficiency of 93 percent. If the unit cost of electricity is $\$ 0.06 / \mathrm{kWh}$, the annual electricity cost of this compressor is $(a) \$ 7802$ $(b) \$ 9021$ $(c) \$ 12,100$ $(d) \$ 8389$ $(e) \$ 10,460$

A 75 -hp compressor in a facility that operates at full load for $2500 \mathrm{h}$ a year is powered by an electric motor that has an efficiency of 93 percent. If the unit cost of electricity is $\$ 0.06 / \mathrm{kWh}$, the annual electricity cost of this compressor is
$(a) \$ 7802$
$(b) \$ 9021$
$(c) \$ 12,100$
$(d) \$ 8389$
$(e) \$ 10,460$

Key Concepts

Cost Calculation

Cost calculation in the context of electricity usage entails multiplying the total energy consumption by the unit cost of electricity. This allows one to estimate the monetary expense associated with operating a device over a certain period, which is a fundamental part of energy budgeting and economic decision-making in both industrial and residential applications.

Energy Consumption Calculation

Calculating energy consumption involves determining the total amount of energy used over a period by combining the power rating (after conversion if necessary) and the operating time. For electrical devices, energy consumption is usually calculated in kilowatt-hours, making it an essential step for assessing overall energy use and planning cost estimates.

Horsepower to Kilowatt Conversion

This concept involves converting power from horsepower to kilowatts, which is necessary because electrical energy usage is typically measured in kilowatt-hours. Understanding that one horsepower is equivalent to approximately 0.746 kilowatts allows for proper calculation of the power input required for electrical devices.

Motor Efficiency

Motor efficiency refers to the ratio of useful mechanical output power to the electrical power input. This concept is crucial when dealing with real-world electrical machines, as it shows that due to losses (typically in the form of heat), the actual electrical energy consumed is higher than the mechanical output energy provided.

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