Sackur-Tetrode equation
The Sackur-Tetrode equation is an expression used in statistical thermodynamics to calculate the entropy of an ideal gas of point particles. The equation was first derived independently by Carl Sackur and Jakob Tetrode in 1912.
The Sackur-Tetrode equation is given by:
S = Nk [ ln(V/N ((4Οmk/h^2)^(3/2)T^(5/2))) + 5/2 ]
where:
S is the entropy of the gas in J/K N is the number of particles in the gas V is the volume of the gas in m^3 m is the mass of a single particle in kg k is the Boltzmann constant (1.380649 × 10^-23 J/K) h is the Planck constant (6.62607015 × 10^-34 J s) T is the absolute temperature of the gas in K
The Sackur-Tetrode equation is an improvement over the simpler Boltzmann equation for the entropy of an ideal gas because it takes into account the quantum mechanical nature of the particles. The equation predicts that the entropy of an ideal gas decreases as the temperature approaches absolute zero, which is known as the third law of thermodynamics.
S = N k (log(V/N ((4 Ο m U)/(3 N h^2))^(3/2)) + 5/2) | S | absolute entropy N | particle number V | volume U | internal energy m | mass of a particle k | Boltzmann constant (≈ 1.381×10^-23 J/K) h | Planck constant (≈ 6.626×10^-34 J s) (assuming a monatomic ideal gas)
particle number | 6.02×10^23 volume | 1 m^3 (cubic meter) internal energy | 3 J (joules) mass of a particle | 1 u (unified atomic mass unit)
absolute entropy | 50.76 J/K (joules per kelvin) = 3.168×10^20 eV/K (electronvolts per kelvin) = 5.076×10^8 erg/K (ergs per kelvin)
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