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Finite systems may undergo first or second order phase transitions under not isovolumetric but isobaric condition. The “analyticity” of a finite-system partition function has been argued to imply universal values for isobaric critical exponents, αP, βP, and γP. Here we test this prediction by analyzing NIST REFPROP data for twenty major molecules, including H2O, CO2, O2, etc. We report they are consistent with the prediction for temperature range, 10-5<|T/Tc-1|<10-3. For each molecule, there appears to exist a characteristic natural number, n = 2, 3, 4, 5, 6, which determines all the critical exponents for T < Tc as αP=γP=nn+1 and βP=δ-1=1n+1. For the opposite T > Tc, all the fluids seem to indicate the universal value of n = 2.