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is the number of gas particles; is the Boltzmann constant (1.381 × 10 −23 J·K −1). The probability distribution of particles by velocity or energy is given by the Maxwell speed distribution. The ideal gas model depends on the following assumptions:
In an ideal solution, the chemical potential of species i (μ i) is dependent on temperature and pressure. μ i0 (T, P) is defined as the chemical potential of pure species i. Given this definition, the chemical potential of species i in an ideal solution is
The total energy of the system at any value of x is given by the internal energy of the gas plus the potential energy of the weight: = + + where T is temperature, S is entropy, P is pressure, μ is the chemical potential, N is the number of particles in the gas, and the volume has been written as V=Ax.
Equilibrium thermal distributions for particles with integer spin (bosons), half integer spin (fermions), and classical (spinless) particles. Average occupancy is shown versus energy relative to the system chemical potential , where is the system temperature, and is the Boltzmann constant.
The number of particles is, like volume and entropy, the displacement variable in a conjugate pair. The generalized force component of this pair is the chemical potential. The chemical potential may be thought of as a force which, when imbalanced, pushes an exchange of particles, either with the surroundings, or between phases inside the system.
The molar gas constant (also known as the gas constant, universal gas constant, or ideal gas constant) is denoted by the symbol R or R. It is the molar equivalent to the Boltzmann constant , expressed in units of energy per temperature increment per amount of substance , rather than energy per temperature increment per particle .
where T = temperature, S = entropy, p = pressure, V = volume. N i is the number of particles of type i in the system and μ i is the chemical potential for an i-type particle.The set of all N i are also included as natural variables but may be ignored when no chemical reactions are occurring which cause them to change.
Thus the Gibbs free energy of a system can be calculated by collecting moles together carefully at a specified T, P and at a constant molar ratio composition (so that the chemical potential does not change as the moles are added together), i.e. = =.