Density fluctuations and the specific heat near the critical point

Abstract

Abstract A physically intuitive relation is developed between the correlation length for density fluctuations and the specific heat near the critical point of a liquid-vapor system. First, the average spatial extension of a fluctuation (the fluctuation volume) is inferred by considering at what point the volume, in which the fluctuation is supposed to occur, becomes so small that the standard formula relating the compressibility to the density fluctuation breaks down, and it is shown that the length of this extension obeys the same scaling law as the correlation length. The fluid is then divided into cells equal to the fluctuation volume, and the number of possible states of the system arising from the fluctuations in these cells is determined and assumed to be a factor in the partition function. The divergent part of the specific heat is then calculated as a function of temperature, and the result is compared with experimental data and shown to fit known scaling relations. The size of the fluctuation volume required to get the correct specific heat is reasonable. Application is also made to a two-dimensional Ising lattice. Finally, the relation between long-range and short-range fluctuation is considered.