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Both are essentially the same, except that the classical thermodynamic ideal gas is based on classical statistical mechanics, and certain thermodynamic parameters such as the entropy are only specified to within an undetermined additive constant. The ideal quantum Boltzmann gas overcomes this limitation by taking the limit of the quantum Bose ...
In the case of an ideal gas, the heat capacity is constant and the ideal gas law PV = nRT gives that α V V = V/T = nR/p, with n the number of moles and R the molar ideal-gas constant. So, the molar entropy of an ideal gas is given by (,) = (,) + . In this expression C P now is the molar heat capacity. The entropy of inhomogeneous ...
The entropy of a given mass does not change during a process that is internally reversible and adiabatic. A process during which the entropy remains constant is called an isentropic process, written Δ s = 0 {\displaystyle \Delta s=0} or s 1 = s 2 {\displaystyle s_{1}=s_{2}} . [ 12 ]
Since entropy is a state function, the entropy change of any process in which temperature and volume both vary is the same as for a path divided into two steps – heating at constant volume and expansion at constant temperature. For an ideal gas, the total entropy change is: [57] = + Similarly if the temperature and pressure of an ...
The Sackur–Tetrode equation is an expression for the entropy of a monatomic ideal gas. [1]It is named for Hugo Martin Tetrode [2] (1895–1931) and Otto Sackur [3] (1880–1914), who developed it independently as a solution of Boltzmann's gas statistics and entropy equations, at about the same time in 1912.
Boltzmann's equation—carved on his gravestone. [1]In statistical mechanics, Boltzmann's equation (also known as the Boltzmann–Planck equation) is a probability equation relating the entropy, also written as , of an ideal gas to the multiplicity (commonly denoted as or ), the number of real microstates corresponding to the gas's macrostate:
Substituting from the ideal gas equation gives finally: = where n = number of moles of gas in the thermodynamic system under consideration and R = universal gas constant. On a per mole basis, the expression for difference in molar heat capacities becomes simply R for ideal gases as follows:
Entropy changes for systems in a canonical state. ... In the case of the ideal gas, ... the thermodynamic definition of entropy is also defined only up to a constant.)