![]() (But this happens only in the $N \to \infty$ limit as discussed e.g. ![]() In phase transitions as common as freezing/melting entropy is even discontinuous thus the criterion. Importantly, entropy is a state function, like temperature or. ) = \lambda S(A_1.,A_n.), \forall \lambda <0$. Entropy is a measure of how dispersed and random the energy and mass of a system are distributed. for a complete set of extensive parameter $A_i$ we have $S(\lambda A_1. Given a discrete random variable, which takes values in the alphabet and is distributed according to : where denotes the sum over the variable's possible values. Entropy is homogeneous in the parameters defined by physical criteria as "extensive". In information theory, the entropy of a random variable is the average level of 'information', 'surprise', or 'uncertainty' inherent to the variable's possible outcomes.Entropy has a finite difference between any two points in the macro parameter space. ![]() In effect 1/ T is an integrating factor which, when it multiplies the inexact differential Q, results in the exact differential Q / T dS. if it is not it might also be because the list of parameters is not complete.) This means that the net change in entropy during a complete cycle is zero, so that entropy is a function of state. Entropy is a single-valued function of the full set of macroscopic parameters.Then the strongest we can say is the following: As observed, Fermis aim to explain entropy (not only its mathematical expression) is reduced to the definition of a state function without concern for its. Let's say our the physical motivation is paramount. So the answer would be: If a well developed model predicting quantitatively the entropy exists and it is confirmed by thorough testing, the entropy qualifies as the unique entropy of the system.Īdditional note: Observed mathematical conditions Instead we define entropic terms based on macroscopic variables of a system, like the followings (examples among the usual ones):įor a perfect gas one can write the entropy per atom of N atoms in volume V as: $$S_ $$īut also a lot of other response coefficient involving temperature as specified e.g. But of course we almost never use this exact form of entropy in studying real systems, as it is impossible to count the microstates by any means. For a given inital state, there can be infinite H H values depending upon what the final state is. For a given final state, there can be infinite H H values depending upon what the inital state was. Where $\Omega$, can be the partition function in an ensemble, or simply the number of microstates within a given macrostate. H H is a function of two states, the initial state and the final state. Limiting the discussion to physics, when studying a physical system, can be a box filled with an ideal gas, a melt of polymers or the state of rods/molecules in a liquid crystalline system, in all such scenarios, there are specific entropic terms that we define in describing the evolution of the system (by including it in the free energy expression).įrom a statistical mechanics point of view, we use Boltzmann's definition of: $$S=k_B \ln\Omega$$ Heat flow ( #q#), e.g.The concept of entropy is very ubiquitous, we learn about its uses starting from Information Theory ( Shannon entropy) up to its basic definition in statistical mechanics in terms of number of micro-states.Path functions are the flip side, and depend on the way the process is performed, even if the start and end points are the same. #DeltaU = q + w# (first law of thermodynamics) Is it true that at the end of a cyclic process, the change in entropy of the of the system and that of its surrounding are both separately zero irrespective of whether the cycle is reversible or not I have two particular cycles in mind-the reversible Carnot cycle and the irreversible hysteresis loop. ![]() We used the statistical definition of entropy and the minimization of the free enthalpy in. When have you ever cared how the volume changed? Have you ever needed to know how the mass changed, as long as it was conserved in a reaction?Īnd the more usual state function quantities are Entropy S, by the way, is not a state function (TS would be one). It is also explained as the measure of molecular disorder of a system, meaning the system is random. You have used all of these in the ideal gas law, chemical reactions, etc. Is entropy a state function Entropy: Entropy is measured using the thermal energy per unit temperature that isnt around when useful work is being done. You know plenty that you may not have identified before. A state function is simply one that depends only on the start and end point, and not the path. ![]()
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