Air enters an adiabatic nozzle steadily at 300 kpa
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Thus, these two equations will yield the same answers assuming p1, p2, h1, h2 , T1 are somehow known or given only for isentropic flows. The second is for an Ideal gas, isentropic, and constant specific heat assumption. . Based on your problem description, the system does not meet the criteria for the second relation. It does not require flow to be reversible. The first equation is the based on the full energy balance with some assumptions that drop out some terms.

The first equation with h1 and h2 in it works for inviscid adiabatic flows with no work done on the fluid by propellers, etc. The second equation works only for isentropic flows - i. If your system was given as isentropic, ideal gas, with constant specific heats, then you could use the second relation you listed. As a result, it will work even across the shock wave. . .

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