Isentropic Compressor Efficiency

The compressor operates at steady state with an initial pressure of 1 bar and temperature of 310 K, and a mass flow rate of 1000 kg/h. It exits at 10 bar with no change in kinetic or potential energy, and no heat transfer. The gas is assumed to be ideal with a constant k value of 1.391. The equation (T2/T1)=(p2/p1)^(k-1)/k is used to find the minimum theoretical power input and exit temperature, as each parcel of gas experiences an adiabatic reversible compression.
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jdawg
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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 Ts2. For this particular problem they used it to find T 2 and I don't understand why.
 
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  • #2
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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FAQ: Isentropic Compressor Efficiency

What is an isentropic compressor efficiency?

An isentropic compressor efficiency is a measure of how well a compressor can convert input energy into output energy without any heat transfer or change in entropy. It represents the ideal performance of a compressor and is expressed as a percentage.

How is isentropic compressor efficiency calculated?

Isentropic compressor efficiency is calculated by dividing the actual compressor work by the ideal compressor work. The ideal compressor work is calculated using the inlet and outlet pressures and temperatures, assuming an isentropic process.

What factors affect isentropic compressor efficiency?

The factors that affect isentropic compressor efficiency include the type and design of the compressor, operating conditions such as inlet and outlet pressures and temperatures, and the type of gas being compressed. Other factors such as mechanical losses and leakage can also impact efficiency.

Why is isentropic compressor efficiency important?

Isentropic compressor efficiency is important because it is a measure of the performance and energy efficiency of a compressor. A higher efficiency means less energy is wasted during the compression process, resulting in cost savings and reduced environmental impact.

What are some ways to improve isentropic compressor efficiency?

Some ways to improve isentropic compressor efficiency include using more efficient compressor designs, optimizing operating conditions, reducing mechanical losses, and regularly maintaining and cleaning the compressor. Properly sizing and matching the compressor to the application can also improve efficiency.

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