A negative change in entropy indicates that the disorder of an isolated system has decreased. For example, the reaction by which liquid water freezes into ice represents an isolated decrease in entropy because liquid particles are more disordered than solid particles.

The heat capacity is a material-dependent object that – as you say – measures the difference in temperature when energy is absorbed by the material. The entropy change is proportional to the heat transfer in a reversible process (at constant temperature!

Heat is the energy that is transferred from one body to another body because the bodies have different temperatures. It is measured in joules. Entropy is a measure of the unavailability of that heat energy to do work. It is measured in joules per kelvin.

Entropy increases as temperature increases. An increase in temperature means that the particles of the substance have greater kinetic energy. The faster moving particles have more disorder than particles that are moving more slowly at a lower temperature.

Like freedom, the entropy of a system increases with the temperature and with volume. The effect of volume is more easily seem in terms of concentration, especially in the case of mixtures. For a certain number of atoms or molecules, an increase in volume results in a decrease in concentration.

Keep in mind that entropy increases with temperature. This can be understood intuitively in the classical picture, as you mention. However, at higher temperatures, a certain amount of heat added to the system causes a smaller change in entropy than the same amount of heat at a lower temperature. The formula is ΔS=QT.

The quantitative relationship between heat transfer and temperature change contains all three factors: Q = mcΔT, where Q is the symbol for heat transfer, m is the mass of the substance, and ΔT is the change in temperature. The symbol c stands for specific heat and depends on the material and phase.

Heat describes the transfer of thermal energy between molecules within a system and is measured in Joules. Heat measures how energy moves or flows. Temperature describes the average kinetic energy of molecules within a material or system and is measured in Celsius (°C), Kelvin(K), Fahrenheit (°F), or Rankine (R).

Entropy increases when a substance is broken up into multiple parts. The process of dissolving increases entropy because the solute particles become separated from one another when a solution is formed. Entropy increases as temperature increases.

Key Takeaways: Calculating Entropy

1. Entropy is a measure of probability and the molecular disorder of a macroscopic system.
2. If each configuration is equally probable, then the entropy is the natural logarithm of the number of configurations, multiplied by Boltzmann’s constant: S = kB ln W.

A cold object in contact with a hot one never gets colder, transferring heat to the hot object and making it hotter. Furthermore, mechanical energy, such as kinetic energy, can be completely converted to thermal energy by friction, but the reverse is impossible.

Gases

Entropy by definition is the degree of randomness in a system. If we look at the three states of matter: Solid, Liquid and Gas, we can see that the gas particles move freely and therefore, the degree of randomness is the highest.

The greater the mass of a particle, the closer together its energy levels. The effect of closeness of energy levels on the entropy is shown in Figure 16.8. This applies in general for any number of particles and any quantity of energy. Therefore, the heavier the molecules of a substance, the larger its molar entropy.

Entropy generally increases in reactions in which the total number of product molecules is greater than the total number of reactant molecules. An exception to this rule is when a gas is being produced from nongaseous reactants.

As well, increasing the volume of a substance increases the number of positions where each molecule could be, which increases the number of microstates. Therefore, any change that results in a higher temperature, more molecules, or a larger volume yields an increase in entropy.

On doubling the volume, there is an entropy increase of kBln2 per molecule. So part of the entropy per molecule is evidently Boltzmann’s constant kB times the logarithm of how much space the molecule moves around in.

For cases involving an isolated system where no energy is exchanged with the surroundings, spontaneous processes are characterized by an increase in entropy. A spontaneous reaction is a chemical reaction which is a spontaneous process under the conditions of interest.

Entropy, S, is a state function and is a measure of disorder or randomness. A positive (+) entropy change means an increase in disorder. The universe tends toward increased entropy. All spontaneous change occurs with an increase in entropy of the universe.