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I'm studying Compressible Fluid Mechanics through the book "Fluid Mechanics", 4 ed., by Frank White. I learnt that a shock wave is an irreversible process that occurs in the flow. Because of that, I expected that relations that consider reversibility as an hypothesis shouldn't be used. Consider for example the expression (9.53) of the book:

$$\frac{s_2-s_1}{c_v}=\ln\left[\frac{p_2}{p_1}\left(\frac{\rho_1}{\rho_2}\right)^k\right]$$

where $1$ is upstream and $2$ is downstream of the shock wave. I found out that this relation is the same as this one:

$$s_2-s_1=c_p\ln\left(\frac{T_2}{T_1}\right)-R\ln\left(\frac{p_2}{p_1}\right)$$

which can be only used if $\delta q=Tds$, i.e., if the flow is reversible. So even if the shock wave is an irreversible process, the expression (9.53), that assumes reversibility, can be used?

Élio Pereira
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  • If the beginning and end states are in equilibrium and a reversible process can connect them then the entropy change between these states are calculable by the Clausius integral $\Delta S = \int_{rev}\frac{\delta q}{T}$ irrespective of whether the other process you are interested in and connecting the states is irreversible or not. – hyportnex Feb 20 '18 at 23:50
  • Shock waves require some form of irreversibility to initiate from a nonlinearly steepening wave, but need not have irreversible energy dissipation to maintain them once formed (this is somewhat beside the point though). See for example: https://physics.stackexchange.com/a/139436/59023 . – honeste_vivere Feb 21 '18 at 00:02

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