Therefore, any change that results in a higher temperature, more molecules, or a larger volume yields an increase in entropy. As well, increasing the volume of a substance increases the number of positions where each molecule could be, which increases the number of microstates. Increasing the number of molecules in a system also increases the number of microstates, as now there are more possible arrangements of the molecules. This increases the number of microstates possible for the system. The following is a detailed description: The increase in the entropy is due to the randomness increase in the product as compared to the reactant. For an isolated system, the entropy is high due to the high disorder. We can estimate changes in entropy qualitatively for some simple processes using the definition of entropy discussed earlier and incorporating Boltzmann’s concept of microstates.Īs a substance is heated, it gains kinetic energy, resulting in increased molecular motion and a broader distribution of molecular speeds. Entropy: It is a measure of the degree of randomness and disorder of the system. ![]() A process that gives an increase in the number of microstates therefore increases the entropy. Microstates is a term used to describe the number of different possible arrangements of molecular position and kinetic energy at a particular thermodynamic state. Where k is the Boltzmann constant (1.38 × 10 −23 J/K), and W is the number of microstates. He developed an equation, known as the Boltzmann equation, which relates entropy to the number of microstates ( W): Ludwig Boltzmann (1844–1906) pioneered the concept that entropy could be calculated by examining the positions and energies of molecules. ![]() The Boltzmann Equation Figure 18.2 “Ludwig Boltzmann” Figure 18.1 “Two-Atom, Double-Flask Diagram.” When the stopcock is opened between the flasks, the two atoms can distribute in four possible ways. Thus we can say that it is entropically favoured for the gas to spontaneously expand and distribute between the two flasks, because the resulting increase in the number of possible arrangements is an increase in the randomness/disorder of the system. If we increased the number of atoms, we would see that the probability of finding all of the atoms in the original flask would decrease dramatically following (½) n, where n is the number of atoms. The likelihood of all atoms being found in their original flask, in this case, is only 1 in 4. If we were to take snapshots over time, we would see that these atoms can have four possible arrangements. When the stopcock is opened, both atoms are free to move around randomly in both flasks. At first, both atoms are contained in only the left flask. The absolute entropy values are: nitrogen: 192 J K-1 mol-1 hydrogen: 131 J K-1 mol-1 ammonia: 193 J K-1 mol-1 On the left hand side there is 1 mole of nitrogen and 3 moles of hydrogen, hence the total absolute entropy on the left hand side 192 + 3(131) 585 J K-1. ![]() In this system, we have placed two atoms of gas, one green and one blue. The Molecular Interpretation of EntropyĬonsider the following system, where two flasks are sealed together and connected by a stopcock (see Figure 18.1 “Two-Atom, Double-Flask Diagram”). These definitions can seem a bit vague or unclear when you are first learning thermodynamics, but we will try to clear this up in the following subsections. Entropy: A measure of the unavailable energy in a closed thermodynamic system that is also usually considered to be a measure of the systems disorder. In this sense, entropy is a measure of uncertainty or randomness. Entropy is also a measure of the number of possible arrangements the atoms in a system can have. But what exactly is entropy? Entropy is typically defined as either the level of randomness (or disorder) of a system or a measure of the energy dispersal of the molecules in the system. The entropy of an object is a measure of the amount of energy which is unavailable to do work. The second law of thermodynamics states that a spontaneous process will increase the entropy of the universe. To assess the spontaneity of a process we must use a thermodynamic quantity known as entropy ( S). To be able to estimate change in entropy qualitatively.To gain an understanding of the Boltzmann equation and the term microstates.To gain an understanding of the term entropy.However, the entropic quantity we have defined is very useful in defining whether a given reaction will occur. It is evident from our experience that ice melts, iron rusts, and gases mix together. This apparent discrepancy in the entropy change between an irreversible and a reversible process becomes clear when considering the changes in entropy of the surrounding and system, as described in the second law of thermodynamics.
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