<=> { ( ∂f/∂x1² ) + ( ∂f/∂x2² ) + ( ∂f/∂x3² ) +. . .+ ( ∂f/∂xn² ) } × (g)^(k × r) = 0
- Formula 1:
* ∆f × (G)^(K × R) = 0
<=> { ( ∂f/∂x1² ) + ( ∂f/∂x2² ) + ( ∂f/∂x3² ) +. . .+ ( ∂f/∂xn² ) } × (G)^(K × R) = 0
Note:
- The gravitational force is represented by the gravitational constant, G = 6.674 × 10^-11 (N × m^2 / Kg^2).
- The electric force is represented by the Coulomb constant, k = 9 × 10^9 (N × m^2 / C^2).
- The thermodynamics of Gas (Qi) is represented by the gas constant, R = 8.314 (J/mol × K).
=> In an n-dimensional space, the higher the energy level in each dimension, the lower the particle density, and the space tends towards a vacuum.
- Formula 2:
* ∆f × N = 0
<=> { ( ∂f/∂x1² ) + ( ∂f/∂x2² ) + ( ∂f/∂x3² ) +. . .+ ( ∂f/∂xn² ) } × No × e^(-m × g × h /Kb × T) = 0
N = No × e^(-m × g × h /Kb × T).
Note:
N and No: Particles density or particles amount at altitude h (m) and at ground level h = 0.
Kb: Boltzmann constant, Kb = 1.38 × 10^-23 (J/K). Boltzmann coefficient: The factor e^(-€/k × T), determines the prevalence of an energy state. At high temperatures, particles easily jump to higher energy levels.
T: Absolute temperature (K).
m: Mass of the particle (Kg).
g: Acceleration due to gravity, g = 9.81 (m/s^2).
h: Height of n n-dimensional space (h1, h2, h3... hn) (m).