Under what polytropic index value (n) is the work done per unit mass during air compression minimized______________?
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Answer: A. 1
Explanation
An isothermal compression process maintains constant temperature with a polytropic index of one. Work done during gas compression is directly proportional to the area under the process curve. Isothermal compression requires the absolute minimum work input compared to adiabatic or polytropic alternatives. Polytropic processes follow the mathematical equation pressure times volume to the power n equals constant. Isothermal expansion or compression transfers heat freely to maintain constant internal gas temperature. Adiabatic compression involves no heat transfer and results in a higher final gas temperature.
Multi-stage compressors utilize intercoolers to approach isothermal compression and save electrical power. Minimizing compression work improves the overall efficiency of industrial gas turbine power plants. Thermodynamic efficiency analyses rely heavily on comparing actual compressor work to isothermal ideals. Polytropic indices of 1.2, 1.3, or 1.4 represent various degrees of polytropic heat transfer. An index of 1.4 corresponds to reversible adiabatic compression for diatomic air. Higher index values result in greater work input requirements per unit mass of gas.
- Subject
- Engineering
- Category
- Mechanical Engineering
- Topic
- —
- Difficulty
- medium
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