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The energy and entropy of unpolarized blackbody thermal radiation, is calculated using the spectral energy and entropy radiance expressions derived by Max Planck [63] using equilibrium statistical mechanics, = (), = ((+) (+) ()) where c is the speed of light, k is the Boltzmann constant, h is the Planck constant, ν is frequency ...
The definition of the Gibbs function is = + where H is the enthalpy defined by: = +. Taking differentials of each definition to find dH and dG, then using the fundamental thermodynamic relation (always true for reversible or irreversible processes): = where S is the entropy, V is volume, (minus sign due to reversibility, in which dU = 0: work other than pressure-volume may be done and is equal ...
Absolute entropy of strontium. The solid line refers to the entropy of strontium in its normal standard state at 1 atm pressure. The dashed line refers to the entropy of strontium vapor in a non-physical state. The standard entropy change for the formation of a compound from the elements, or for any standard reaction is designated ΔS° form or ...
For an open thermodynamic system in which heat and work are transferred by paths separate from the paths for transfer of matter, using this generic balance equation, with respect to the rate of change with time of the extensive quantity entropy , the entropy balance equation is: [53] [54] [note 1] = = ˙ ^ + ˙ + ˙ where = ˙ ^ is the net rate ...
where S is the entropy of the system, k B is the Boltzmann constant, and Ω the number of microstates. At absolute zero there is only 1 microstate possible ( Ω = 1 as all the atoms are identical for a pure substance, and as a result all orders are identical as there is only one combination) and ln ( 1 ) = 0 {\displaystyle \ln(1)=0} .
It is in this sense that entropy is a measure of the energy in a system that cannot be used to do work. An irreversible process degrades the performance of a thermodynamic system, designed to do work or produce cooling, and results in entropy production. The entropy generation during a reversible process is zero. Thus entropy production is a ...
The entropy of the system may likewise be written as a function of the other extensive parameters as (,,, … ) {\displaystyle S(U,X_{1},X_{2},\dots )} . Suppose that X is one of the X i {\displaystyle X_{i}} which varies as a system approaches equilibrium, and that it is the only such parameter which is varying.