The remaining bulk thermodynamic exponent a determines the rate of divergence of the constant-volume heat capacity Cv at the liquid-vapour critical point of a one-component fluid [or that of the constant-pressure heat capacity Cp, or of the literal mechanical (rather than osmotic) compressibility k, or of the coefficient of thermal expansion, of a liquid mixture near its consolute point]. At fixed p = p , the heat capacity Cv as a function of temperature has the shape shown schematically in Fig. 9.3(a) with [Pg.262]

At a eritieal point, the phase transition under consideration is the second-order transition. For the uniform system, in the critical region the correlation length of statistical fluctuations, the isothermal compressibility and the heat capacity diverge to the infinity, according to the well-known power laws [337]. Moreover, the order parameter, which, for the gas-Uquid transition, is defined as the difference between the densities of both coexisting phases, approaches zero at the critical temperature. [Pg.157]

Experimentally, it is well established that asymptotically close to the critical point all physical properties obey simple power laws. The universal powers in these laws are called critical exponents, the values of which can be calculated from RG recursion relations. The phenomenological approach that interrelates the critical power laws is called scaling theory. In particular, the isochoric heat capacity diverges at the vapour-liquid critical point of one-component fluids along the critical isochore as [Pg.191]

On the basis of this brief summary of RPM criticality, one might be tempted to conclude that the problem has been solved all finite-size scaling analysis point towards the Ising universality class. There is, however, one critical phenomenon which does not seem to have been demonstrated unambiguously in the RPM. This is the critical divergence of the constant-volume heat capacity, Cy. Recall that on the critical isochore and close to the critical temperature where the parameter t = (T — Tc)/Tc is small, [Pg.184]

Contrary to the tail of the correlation function, which is directly connected with the strong divergence of the compressibility, the tirst peak of the correlation function, as pointed out by Stell and H0ye [11), bears a subtle relation to the internal energy. The latter property behaves smoothly at the critical point, but its first temperature derivative, the heat capacity Cv, has a weak divergence. [Pg.12]

However, just as is the case for many other kinds of critical phenomena (e.g. the one-component fluid, magnetism, order-disorder transitions in solids, etc.) such predictions do not agree either with the results of careful experimental measurements or with simple theoretical models that can be treated nearly exactly. The coexistence curve is more nearly cubic than parabolic, the critical isotherm is of distinctly higher order than cubic, and the heat capacity Cp,x,m diverges at the critical point. [Pg.243]

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