Isothermal compressibility coefficient

Here, V refers to the molar volume of the nonelectrolyte, V and Vs° are the intrinsic3 and apparent molar volume of the salt, respectively, and /3 is the isothermic compressibility coefficient of the solution. Although this equation is strictly valid in the limit of Vi - 0 and ca - 0, it works quite satisfactorily for small nonpolar solutes. The equation shows that the effect is greatest for nonelectrolytes of large molar volume Vi, and for salts that cause the largest electrostriction, Vs - Vs°. A difficulty with this expression is that it is not always easy to evaluate the intrinsic volume of a salt (the mere volume, without... 

Table 5.64 lists isobaric thermal expansion and isothermal compressibility coefficients for feldspars. Due to the clear discrepancies existing among the various sources, values have been arbitrarily rounded off to the first decimal place. 

Some isothermal compressibility coefficients in atm.-i multiplied by 10 are given on page 62. ... 

The molar volume change in ionization reactions at higher temperatures and pressures cannot be calculated for most of the aqueous complexes because of a lack of data on isobaric expansion and isothermal compressibility coefficients. Entropy and heat capacity correlations have recently been used to generate equation of state parameters for estimating molal volumes of aqueous complexes at elevated temperatures and pressures (Sverjensky, 12). These coefficients are available for aqueous complexes only of univalent anions and, therefore, the pressure dependence of ionization constants at elevated temperatures cannot be estimated using Equation 4. 

This table gives data on the variation of the density of some common liquids with pressure and temperature. The pressure dependence is described to first order by the isothermal compressibility coefficient i< defined as... 

The final table gives the cubic thermal expansion coefficient a, the isothermal compressibility coefficient and the speed of sound u for liquid mercury as a function of temperature. These properties are defined as follows ... 

Estimate the change of volume of water between two states by isobaric heating from T to T2 at Pi followed by isothermal expansion from Pi to P3 at T2 (a) by using van der Waals equation of state, (b) by using the thermal expansion and isothermal compression coefficients, (c) compare the results of part a and part b. 

The strength of the conservative foree field ean be obtained from the requirement that the density fluctuations of the real fluid should be reproduced. As the static structure faetor for a eoarse-grained system is smaller than that of the atomic system by a faetor n ,ap for low wave numbers, it follows that (pkBTiCT)opo = n p(pkBTKT)a,om- The isothermal compressibility coefficient Kp of the DPD fluid is readily obtained from its surprisingly simple equation of state [24], p apk T-l-O.lap, and this set of equations is then solved for a. 

Isothermal compressibility coefficient at constant temperature T It is defined by relation ... 

The two right-hand-most columns gives values of the isothermal compressibility coefficient, = - l/V) dV/dP) = (l/p) dp/dP) and the isobaric cubic expansion coefficient, = (l/V)(dV/dT)p = - llp) dpldT)j, calculated for T = 298.15 K andP = 0.101325 MPa from the Tait Eq. 1 and from the p (T, P ) equation, respectively. In a very few cases when the lower temperature limit of the Tait equation is greater than 298.15 K, the extrapolated values of isothermal compressibility are given. 

Table 2.10 The isentropic and isothermal compressibility coefficients of water and citric acid solutions as function of concentration and temperature... 

Knowing values of the isothermal compressibility coefficients K T m) and the cubic expansion coefficients a T,m) it is possible from the thermodynamic relation... 

Other compressibility parameters, like the isothermal compressibility coefficients, are not available because the specific heats of solutions are nnknown. 

The SmC-N transition volumes are an order of magnitude larger than those of the N,g-SmA transition. For theoretical considerations the isothermal compressibility coefficient and the parameter... 

The variations in the N-I transition volumes and the isothermal compressibility coefficients of the different compounds can be attributed to a large extent to the effects of end chain flexibility. The N (N )-I transition volumes of CBOOA and CN decrease more rapidly with increasing transition temperature than that of the relatively inflexible MBBA. 

Isothermal compressibility coefficient 3 = Note isothermal means constant T. 

---