Isentropic Compressor Efficiency

[jdawg]

Homework Statement

Nitrogen enters an insulated compressor operating at steady state at 1 bar, 310 K with a mass flow rate of 1000 kg/h and exits at 10 bar. Change in KE and PE is zero. Heat transfer is zero. Assume ideal gas with k=1.391.

Find minimum theoretical power input required and the exit temperature.

Homework Equations

The Attempt at a Solution

Ok, so I'm very confused about this equation: (T₂/T₁)=(p₂/p₁)^(k-1)/k.

Sometimes my homework solutions will use this equation to get the real value of T₂, and sometimes they will use it to find the ideal property T_s2. For this particular problem they used it to find T ₂ and I don't understand why.

 

[Chestermiller]

The key words are "minimum theoretical power input." This tells you that each parcel of gas passing through the compressor experiences basically an adiabatic reversible compression (since this requires minimum work).

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