How Can I Determine the Compressor Exit Temperature?

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In the discussion on product compression, the main focus is on determining the outlet temperature of a compressed gas when the inlet flow rate, pressure, and temperature, as well as the outlet pressure and flow rate, are known. The initial approach using the ideal gas law (P1V1/T1 = P2V2/T2) leads to complications due to the dependency of volume on temperature, resulting in oscillating calculations. A recommended method involves using the T-dS equations for isentropic flow with constant specific heat, specifically the relationship between pressures and temperatures expressed as (P1/P2) = (T1/T2)^(γ/(γ-1)), which provides a more stable calculation for the outlet temperature based on the type of compressor and process involved.
thearny
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Product Compression. I am currently doing some work on compression. I know the flowrate in and the pressure and temperature in, and I know the pressure (and flowrate) out. Can I determine the temperature out?

I have tried using P1V1/T1=P2V2/T2, but as V is a function of T (using values from Perry's) I have ended up in iterative cycle in which the exit T is oscillating increasingly wildly with time.

What is the best approach to these calculations?

Thanks in advance.
 
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The "best" approach definitely depends on the type of compressor and the process being undertaken.

If you want a place to start, you can look at the T-dS equations for isentropic flow with constant specific heat to come up with:

\frac{p_1}{p_2}=\left[\frac{T_1}{T_2}\right]^{\frac{\gamma}{\gamma-1}}
 
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