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__real inert gas__(i.e. nitrogen N2) being compressed in a piston-like configuration, I'd like to estimate the peak pressure and peak temperature at the instant the gas is brought to full compression.

Initial pressure and initial temperature (in the uncompressed state) are known: typically, ##P_{in}=200## bar and ##T_{in}=20##°C (room temperature).

I assume there is no heat exchange between the gas and the walls of the piston/cylinder (I guess it is reasonable in case of a "fast compression").

Compression ratio (volumetric) is typically ##2##, and gas compression is typically carried out in a few tenths of a second.

*****Question no. 1:**With those assumptions, I guess the process can be considered as isentropic. Is it true? In case of a real inert gas, how fast is too fast in order to consider the compression as a sequence of quasi-equilibrium states? (more about that to follow...)

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I'm interested in the

__real__gas behaviour.

Hence, I'm considering the compressibility factor ##Z(P,T)## and the "real gas law":

$$PV=Z(P,T)nRT$$

Additionally, I'm considering the real specific heat capacity ##c_v(P,T)##.

For both, I'm using accurate values from the NIST database. I have already verified with practical experiments that the use of such values of the ##Z##-factor works great with "static"/isothermal compressions.

Now, in an isentropic process we have (please do not consider the signs, as I'm only interested in the absolute values of the quantities):

$$dU=dW=PdV$$

$$dU=nc_vdT$$

Hence:

$$dT=\frac{PdV}{nc_v}$$

Now, I'm calculating the pressure and temperature increase during compression numerically.

I divide my compression stroke length in many "small stroke intervals" (each corresponding to a certain volume ##V##, so that the difference between each is a small ##dV##).

For each interval I assume constant ##P## and constant ##T## and:

- I solve the "real gas law" (with the use of the proper ##Z##-factor according to the specific pressure and temperature resulting from the previous interval) in order to find the pressure ##P## for the current interval
- I calculate the small temperature increase ##dT## which I will add (to the temperature used for the current interval) for the calculations for the next interval (again, I'm using the proper real value for ##c_v## according to the specific pressure and temperature being considered)

*****Question no. 2:**Also with reference to question no.1 and to the next questions, is this a valid approximation of what happens in reality? Please remember I'm considering an inert gas.

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***Question no. 3:I expect some work ##dW## is lost during compression because of internal turbulence/friction between the gas molecules (or between the gas molecules and the piston-cylinder system walls) but – as for my purposes – could the missing increase in temperature due to the loss of work be compensated by the increase in temperature due to the turbulence/friction (hence leading more or less to the same final result)?

***Question no. 3:

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***Question no. 4:As per my assumptions, the gas temperature when the gas is brought back to the uncompressed state (following a compression cycle) should be the same as the initial temperature before the first compression cycle. In the real world situation – but always assuming no exchange of heat from the gas – would the temperature, after many compression+decompression cycles, progressively build up because of the friction between the gas molecules (or between the gas molecules and the piston-cylinder system walls)?

***Question no. 4:

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Thanks for your attention.