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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 ...
To derive the ideal gas law one does not need to know all 6 formulas, one can just know 3 and with those derive the rest or just one more to be able to get the ideal gas law, which needs 4. Since each formula only holds when only the state variables involved in said formula change while the others (which are a property of the gas but are not ...
Ideal gas equations Physical situation Nomenclature Equations Ideal gas law: p = pressure; V = volume of container; T = temperature; ... Entropy change
The properties of molar internal energy and entropy —defined by the first and second laws of thermodynamics, hence all thermodynamic properties of a simple compressible substance—can be specified, up to a constant of integration, by two measurable functions: a mechanical equation of state = (,) , and a constant volume specific heat
The ideal gas law is the equation of state for an ideal gas, given by: = where P is the pressure; V is the volume; n is the amount of substance of the gas (in moles) T is the absolute temperature; R is the gas constant, which must be expressed in units consistent with those chosen for pressure, volume and temperature.
The Van 't Hoff equation relates the change in the equilibrium constant, K eq, of a chemical reaction to the change in temperature, T, given the standard enthalpy change, Δ r H ⊖, for the process. The subscript r {\displaystyle r} means "reaction" and the superscript ⊖ {\displaystyle \ominus } means "standard".
Since an entropy is a state function, the entropy change of the system for an irreversible path is the same as for a reversible path between the same two states. [23] However, the heat transferred to or from the surroundings is different as well as its entropy change. We can calculate the change of entropy only by integrating the above formula.
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 ...