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I just want to double check something: My understanding is that the higher the compression pressure the higher the amount of energy per unit mass it will take to compress a given mass of gas.

So my question is, would a decoupled system where the compression can take place over a longer time period and at lower pressures (case1) be more efficient than one where the compression takes place at the same rate of expansion (case2)?

Here is a bullet point description of my two scenarios:

case 1:

Compressor inlet pressure = 1 bar

Compressor outlet pressure = 50 bar

compression time = t

compression mass rate = x

Turbine inlet pressure = 45 bar

Turbine outlet pressure = 1 bar

Expansion time = t/2

Expansion mass rate = 2x

case 2:

Compressor inlet pressure = 1 bar

Compressor outlet pressure = 100 bar

compression time = t/2

compression mass rate = 2x

Turbine inlet pressure = 45 bar

Turbine outlet pressure = 1 bar

Expansion time = t/2

Expansion mass rate = 2x

Thank you for your help