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The chemical potentials of bosons and fermions is related to the number of particles and the ... the chemical potential of species i in an ideal ... gas constant, and ...
μ is the chemical potential, k is the Boltzmann constant, T is absolute temperature, N is the total number of particles: =, Z is the partition function: = /, e is Euler's number; Equivalently, the number of particles is sometimes expressed as
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:
The kinetic theory of gases applies to the classical ideal gas, which is an idealization of real gases. In real gases, there are various effects (e.g., van der Waals interactions , vortical flow, relativistic speed limits, and quantum exchange interactions ) that can make their speed distribution different from the Maxwell–Boltzmann form.
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.
Chemical potential / Particle number; ... variables held constant. For every thermodynamic potential ... gas, then the number of particles N is also a natural ...
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 .
The thermodynamics of an ideal Bose gas is best calculated using the grand canonical ensemble.The grand potential for a Bose gas is given by: = = (). where each term in the sum corresponds to a particular single-particle energy level ε i; g i is the number of states with energy ε i; z is the absolute activity (or "fugacity"), which may also be expressed in terms of the chemical ...