Milivoje M. Kostic e-mail: kostic@niu.edu Northern Illinois University, DeKalb, IL 60115-2854 Analysis of Enthalpy Approximation for Compressed Liquid Water It is custom to approximate solid and liquid thermodynamic properties as being a func- tion of temperature only, since they are virtually incompressible, and Pdv boundary work may be neglected. Furthermore, in classical literature, for isothermal compression pro- cesses, a general “improvement” and correction for liquid enthalpy approximation is given by adding the “pressure correction,” vdP, to the corresponding saturation value. It is shown that such correction given for isothermal processes is generally valid for isen- tropic processes only. Analysis of water real properties, over the saturation temperature range and a wide pressure range up to 100 MPa, shows that the recommended correc- tions are only beneficial for higher pressures at smaller temperatures (below 200 ° C), insignificant for smaller pressures at most of the temperatures, about the same but op- posite sign (thus unnecessary) for intermediate temperatures and pressures, and more erroneous (thus counterproductive and misleading) for higher temperatures and pres- sures, than the corresponding saturation values without any correction. The misconcep- tion in the literature is a result of the erroneous assumption, that due to incompressibility for liquids in general, the internal energy is less dependent on pressure than enthalpy. DOI: 10.1115/1.2175090 Keywords: enthalpy, water, thermodynamic properties, thermodynamic analysis, isothermal, isentropic 1 Introduction Since solids and liquids are virtually but not exactly incom- pressible, then the compression work, Pdv, could be neglected and thus many properties virtually will not be a function of pressure but temperature only, such as specific internal energy, u, etc. Fur- thermore, any process is also at the same time an isochoric, constant-volume process. Namely, the isobaric, constant-pressure process will be a simultaneously constant-volume process for an incompressible substance, so that specific heat at constant pres- sure, c p , and constant volume, c v , are the same, or approximately the same for virtually incompressible real solids and liquids, par- ticularly when compared to vapors and gases, i.e.: u  uT u sat T and c p  c v  cT 1 Even the specific enthalpy for a liquid from here on word “spe- cific” will be assumed and omitted for brevity, can be approxi- mated to be independent from pressure and conveniently taken to be equal to the corresponding saturated liquid value at the given temperature: h P, T hT h sat T 2 However, enthalpy is unique, since it is explicitly defined as a function of pressure, namely: h  u + P · v thus, hT, P = uT, P + P · v  u sat T + P · v 3 Therefore, it is common in most engineering references, including classical and widely used thermodynamics textbooks 1,2, to evaluate the change of enthalpy, assuming incompressibility dv =0, but taking correction for pressure increase as: 4 Furthermore, for isothermal processes dT =0 and du  0, then dh  vdP, and finally, for finite pressure difference change from saturated pressure, P sat , corresponding to the given temperature, T, the specific enthalpy with correction, h corr T , P at that tem- perature, T, and any pressure, P, will be 1,2: 5a 5b where, h sat T and v sat T are liquid saturation enthalpy and liquid saturation specific volume at given temperature, T, respectively. It is stated in many references, including 1,2, that the above equa- tions 5a and 5b are recommended as the correction for isother- mal, liquid enthalpy dependence on pressure, and that it is more accurate than a simple, approximation without correction, h sat Eq. 2. It is the objective of this paper to point out the erroneous gen- eral recommendations in the literature. The correction Eq. 5, as recommended in many references, is only useful for higher pres- sures at smaller temperatures, but is actually more erroneous thus counterproductive and misleading for higher temperatures and pressures, and is about the same but opposite sign, thus not nec- essary for intermediate temperatures, than the simple approxima- tion Eq. 2 without any correction. Corresponding analysis us- ing real water data 3 and physical justification are presented below. Contributed by the Heat Transfer Division of ASME for publication in the JOUR- NAL OF HEAT TRANSFER. Manuscript received December 13, 2004; final manuscript received November 1, 2005. Review conducted by John H. Lienhard V. Paper pre- sented at the 2004 ASME International Mechanical Engineering Congress IM- ECE2004, November 13–19, 2004, Anaheim, California, USA. Journal of Heat Transfer MAY 2006, Vol. 128 / 421 Copyright © 2006 by ASME