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The classical ideal gas can be separated into two types: The classical thermodynamic ideal gas and the ideal quantum Boltzmann gas. 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 ...
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.
Isotherms of an ideal gas for different temperatures. The curved lines are rectangular hyperbolae of the form y = a/x. They represent the relationship between pressure (on the vertical axis) and volume (on the horizontal axis) for an ideal gas at different temperatures: lines that are farther away from the origin (that is, lines that are nearer to the top right-hand corner of the diagram ...
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 ...
Boltzmann's entropy formula—carved on his gravestone. [1]In statistical mechanics, Boltzmann's entropy formula (also known as the Boltzmann–Planck equation, not to be confused with the more general Boltzmann equation, which is a partial differential equation) is a probability equation relating the entropy, also written as , of an ideal gas to the multiplicity (commonly denoted as or ), the ...
Below are useful results from the Maxwell–Boltzmann distribution for an ideal gas, and the implications of the Entropy quantity. The distribution is valid for atoms or molecules constituting ideal gases.
In thermodynamics, the entropy of mixing is the increase in the total entropy when several initially separate systems of different composition, each in a thermodynamic state of internal equilibrium, are mixed without chemical reaction by the thermodynamic operation of removal of impermeable partition(s) between them, followed by a time for establishment of a new thermodynamic state of internal ...
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 ]