Abstract
A generalization of the Lambert W function called the logarithmic Lambert function is introduced and is found to be a solution to the thermostatistics of the three-parameter entropy of classical ideal gas in adiabatic ensembles. The derivative, integral, Taylor series, approximation formula, and branches of the function are obtained. The heat functions and specific heats are computed using the “unphysical” temperature and expressed in terms of the logarithmic Lambert function.
Highlights
The first law of thermodynamics [1] states that the total energy of a system remains constant, even if it is converted from one form to another
Experience indicates that only certain states occur. This eventually leads to the second law of thermodynamics and the definition of another state variable called entropy
The goal of this paper is to introduce a generalized Lambert W function and derive its applications to the adiabatic thermostatistics of the three-parameter entropy of classical ideal gas
Summary
The first law of thermodynamics [1] states that the total energy of a system remains constant, even if it is converted from one form to another. The specific form of each of the four adiabatic ensembles and its heat function and corresponding entropy are listed in Table 1 (see [3]). The goal of this paper is to introduce a generalized Lambert W function and derive its applications to the adiabatic thermostatistics of the three-parameter entropy of classical ideal gas. This generalized Lambert W function will be called the logarithmic Lambert function. The properties of the logarithmic Lambert function have implications in the applications to the adiabatic thermostatistics of the three-parameter entropy of classical ideal gas.
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