2025 Volume 20 Issue 1 Pages 36-45
In the extended Dowson-Higginson density equation in the second report, it was found that the reciprocal of the density increase ratio, 1/(ρpt/ρ0t−1), is proportional to the reciprocal of the pressure temperature, 1/PT. However, it was difficult to understand the physical meaning of the proportional relationship between these two reciprocals. Therefore, in this report, we examined whether a linear equation could be constructed for the relationship between the dimensionless density ρpt/ρ0t and the pressure temperature product PT. As a result, it was found that the dimensionless density 6th power (ρpt/ρ0t)6 has a linear relationship with the pressure temperature product PT. We derived the linear equation (ρpt/ρ0t)6=εPT+1. Considering the physical meaning of the derived equation, the dimensionless density cube (ρpt/ρ0t)3 squared (=density substitute function square) corresponds to the pressure temperature product PT. For that reason, it can be understood that the linearization was caused by the dimensionless density 6th power (ρpt/ρ0t)6. This is similar to the linearization of the extended Barus equation in the first report. Since the dimensionless density ρpt/ρ0t is unitless and the value itself is one-dimensional, the three-dimensionalization is required to express the characteristics as a substitute function of density. It was consistent with what we assumed to be.
