Compressor work is minimized when the adiabatic index n equals_________________?
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Answer: B. 1
Explanation
Polytropic compression work depends directly on the adiabatic index n used in the process equation. An index value of n equal to one corresponds mathematically to an isothermal compression process. Isothermal compression requires the minimum work input because heat is removed to keep temperature constant. Polytropic processes follow the general relation where pressure multiplied by volume to the power n is constant. Adiabatic compression has an index equal to the ratio of specific heats, requiring much higher work input. Isothermal compression maintains constant temperature by rejecting heat continuously during the working stroke.
Multi-stage compressors utilize intercoolers to approach isothermal compression and reduce total power consumption. Minimizing compressor work improves the overall efficiency of industrial gas compression and refrigeration plants. Energy conservation principles dictate that isothermal paths require the least mechanical shaft work input. Option A suggests an index below one, which does not represent standard compression work minimization. Option C represents a typical polytropic exponent for air compressors, which requires more work than isothermal. Option E represents severe polytropic compression with high work requirements and significant temperature spikes.
- Subject
- Engineering
- Category
- Mechanical Engineering
- Topic
- —
- Difficulty
- medium
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