### Entropy Changes in an Ideal Gas

Dec 20, if there is a decrease in pressure at constant temperature will there be an increase in entropy?. the entropy and the volume, this relation is valid and then the entropy, pressure and temperature. Mar 22, How pressure, temperature and volume affect Entropy (and Enthalpy) is illustrated by a simple Here are some of the math relationships that include entropy.

The statistical mechanics description of the behavior of a system is necessary as the definition of the properties of a system using classical thermodynamics becomes an increasingly unreliable method of predicting the final state of a system that is subject to some process.

Function of state[ edit ] There are many thermodynamic properties that are functions of state. This means that at a particular thermodynamic state which should not be confused with the microscopic state of a systemthese properties have a certain value.

Often, if two properties of the system are determined, then the state is determined and the other properties' values can also be determined.

**How To Calculate Entropy Changes: Mixing Ideal Gases**

For instance, a quantity of gas at a particular temperature and pressure has its state fixed by those values and thus has a specific volume that is determined by those values. As another instance, a system composed of a pure substance of a single phase at a particular uniform temperature and pressure is determined and is thus a particular state and is at not only a particular volume but also at a particular entropy.

## Thermodynamic equations

In the Carnot cycle, the working fluid returns to the same state it had at the start of the cycle, hence the line integral of any state function, such as entropy, over this reversible cycle is zero.

Reversible process[ edit ] Entropy is conserved for a reversible process.

A reversible process is one that does not deviate from thermodynamic equilibrium, while producing the maximum work. Any process which happens quickly enough to deviate from thermal equilibrium cannot be reversible.

### Pressure and the Thermodynamic Identity

In these cases energy is lost to heat, total entropy increases, and the potential for maximum work to be done in the transition is also lost. More specifically, total entropy is conserved in a reversible process and not conserved in an irreversible process.

An irreversible process increases entropy. According to Carnot's principle, work can only be produced by the system when there is a temperature difference, and the work should be some function of the difference in temperature and the heat absorbed QH.

Carnot did not distinguish between QH and QC, since he was using the incorrect hypothesis that caloric theory was valid, and hence heat was conserved the incorrect assumption that QH and QC were equal when, in fact, QH is greater than QC.

Extensive parameters are properties of the entire system, as contrasted with intensive parameters which can be defined at a single point, such as temperature and pressure.

The extensive parameters except entropy are generally conserved in some way as long as the system is "insulated" to changes to that parameter from the outside. The truth of this statement for volume is trivial, for particles one might say that the total particle number of each atomic element is conserved.

In the case of energy, the statement of the conservation of energy is known as the first law of thermodynamics. A thermodynamic system is in equilibrium when it is no longer changing in time. This may happen in a very short time, or it may happen with glacial slowness.

### Thermodynamic equations - Wikipedia

A thermodynamic system may be composed of many subsystems which may or may not be "insulated" from each other with respect to the various extensive quantities.

If we have a thermodynamic system in equilibrium in which we relax some of its constraints, it will move to a new equilibrium state.

The thermodynamic parameters may now be thought of as variables and the state may be thought of as a particular point in a space of thermodynamic parameters. The change in the state of the system can be seen as a path in this state space.