# Temperature and entropy relationship

### Entropy and temperature | Physics Forums

Temperature is then defined as the thermodynamic quantity that is the That is, the connection of entropy with information works both ways;. When a high temperature object is placed in contact with a low temperature object, then energy will flow from the The Relationship of Entropy to Temperature. Heat added to a system at a lower temperature causes higher entropy .. In the following I'll detail the relationship between Q and S, and then T and S, for a.

We noted that the cumulative amount of heat transfer and the cumulative amount of work done over an entire process path are given by the two integrals: The discovery of the Second Law came about in the 19th century, and involved contributions by many brilliant scientists.

There have been many statements of the Second Law over the years, couched in complicated language and multi-word sentences, typically involving heat reservoirs, Carnot engines, and the like.

### The Relationship between Entropy and Temperature – fabula-fantasia.info

These statements have been a source of unending confusion for students of thermodynamics for over a hundred years. What has been sorely needed is a precise mathematical definition of the Second Law that avoids all the complicated rhetoric.

The sad part about all this is that such a precise definition has existed all along. The definition was formulated by Clausius back in the 's. Clausius wondered what would happen if he evaluated the following integral over each of the possible process paths between the initial and final equilibrium states of a closed system: He carried out extensive calculations on many systems undergoing a variety of both reversible and irreversible paths and discovered something astonishing.

He found that, for any closed system, the values calculated for the integral over all the possible reversible and irreversible paths between the initial and final equilibrium states was not arbitrary; instead, there was a unique upper bound maximum to the value of the integral. Clausius also found that this result was consistent with all the "word definitions" of the Second Law.

## Entropy and temperature

Clearly, if there was an upper bound for this integral, this upper bound had to depend only on the two equilibrium states, and not on the path between them. It must therefore be regarded as a point function of state. Clausius named this point function Entropy. But how could the value of this point function be determined without evaluating the integral over every possible process path between the initial and final equilibrium states to find the maximum?

Clausius made another discovery. He determined that, out of the infinite number of possible process paths, there existed a well-defined subset, each member of which gave the same maximum value for the integral.

### fabula-fantasia.info: Thermodynamics & Heat: Entropy

This is a common confusion. Entropy To specify the precise state of a classical system, you need to know its location in phase space. For a bunch of helium atoms whizzing around in a box, phase space is the position and momentum of each helium atom.

Lets say you know the total energy of the gas, but nothing else. It will be the case that a fantastically huge number of points in phase space will be consistent with that energy.

The entropy of a uniform distribution is the logarithm of the number of points, so that's that. If you also know the volume, then the number of points in phase space consistent with both the energy and volume is necessarily smaller, so the entropy is smaller.

## Entropy and Temperature

This might be confusing to chemists, since they memorized a formula for the entropy of an ideal gas, and it's ostensibly objective. Someone with perfect knowledge of the system will calculate the same number on the right side of that equation, but to them, that number isn't the entropy.

**Thermodynamics # Entropy Change in terms of Temperature and Pressure # Lecture**

It's the entropy of the gas if you know nothing more than energy, volume, and number of particles. Temperature The existence of temperature follows from the zeroth and second laws of thermodynamics: Temperature is then defined as the thermodynamic quantity that is the shared by systems in equilibrium. This is wrong as a definition, for the same reason that the ideal gas entropy isn't the definition of entropy.

Probability is in the mind. Entropy is a function of probabilities, so entropy is in the mind.