# 21: Entropy and the Third Law of Thermodynamics

- Page ID
- 11817

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- 21.1: Entropy Increases With Increasing Temperature
- The entropy of a system increases with temperature and can be calculated as a function of temperature if we know the heat capacity of the system.

- 21.2: The 3rd Law of Thermodynamics Puts Entropy on an Absolute Scale
- The 3rd law of thermodynamics says that a perfect (100% pure) crystalline structure at absolute zero (0 K) will have no entropy (\(S\)). Note that if the structure in question were not totally crystalline, then although it would only have an extremely small disorder (entropy) in space, we could not precisely say it had no entropy. We can put entropy on an absolute scale.

- 21.3: The Entropy of a Phase Transition can be Calculated from the Enthalpy of the Phase Transition
- For a general phase transition at equilibrium and constant temperature and pressure: \(\frac{\Delta_{trs}H}{T_{trs}}=\Delta_{trs}S\).

- 21.4: The Debye Function is Used to Calculate the Heat Capacity at Low Temperatures
- The 3rd law of thermodynamics will essentially allow us to quality the absolute amplitude of entropies. It says that when we are considering a totally perfect (100% pure) crystalline structure, at absolute zero (0 Kelvin), it will have no entropy (S). Note that if the structure in question were not totally crystalline, then although it would only have an extremely small disorder (entropy) in space, we could not precisely say it had no entropy.

- 21.5: Practical Absolute Entropies Can Be Determined Calorimetrically
- By measuring the heat capacities and enthalpies of transitions for a substance, the practical entropy can be calculated for any temperature.

- 21.6: Practical Absolute Entropies of Gases Can Be Calculated from Partition Functions
- If the partition function, \(Q\) is known for a system, the practical absolute entropy of the system can calculated.

- 21.7: Standard Entropies Depend Upon Molecular Mass and Structure
- Entropy is related to the number of microstates a collection of particles can occupy. As both the molecular mass and molecular structure of the particles will affect the number of available microstates, they also affect the entropy of the collection of particles. In general, the entropy of a system increases with molecular mass and the number of atoms in a molecule.

- 21.8: Spectroscopic Entropies sometimes disgree with Calorimetric Entropies
- Some substances have residual entropy that arises when multiple configurations exist for the structure of the substance at zero kelvin.

- 21.9: Standard Entropies Can Be Used to Calculate Entropy Changes of Chemical Reactions
- Since entropy is a state function (path independent), we can calculate entropy changes in a chemical reaction by taking the sum of the standard entropies of the products and subtracting the sum of the standard entropies of the reactants.