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Standard molar entropy
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==Thermodynamics== If a [[mole (unit)|mole]] of a solid substance is a perfectly ordered solid at 0{{nbsp}}K, then if the solid is warmed by its surroundings to 298.15{{nbsp}}K without melting, its absolute molar entropy would be the sum of a series of {{mvar|N}} stepwise and reversible entropy changes. The limit of this sum as <math>N \rightarrow \infty </math> becomes an integral: :<math>S^\circ = \sum_{k=1}^N \Delta S_k = \sum_{k=1}^N \frac{dQ_k}{T} \rightarrow \int _0 ^{T_2} \frac{dS}{dT} dT = \int _0 ^{T_2} \frac {C_{p_k}}{T} dT</math> In this example, <math>T_2 =298.15 K </math> and <math>C_{p_k}</math> is the [[molar heat capacity]] at a constant pressure of the substance in the [[reversible process (thermodynamics)|reversible process]] {{mvar|k}}. The molar heat capacity is not constant during the experiment because it changes depending on the (increasing) temperature of the substance. Therefore, a table of values for <math>\frac{C_{p_k}}{T}</math> is required to find the total molar entropy. The quantity <math>\frac{dQ_{k}}{T}</math> represents the ratio of a very small exchange of heat energy to the temperature {{mvar|T}}. The total molar entropy is the sum of many small changes in molar entropy, where each small change can be considered a reversible process.
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