Relationship between entropy and temperature

homework and exercises - A relationship between entropy and temperature - Physics Stack Exchange

relationship between entropy and temperature

Temperature is then defined as the thermodynamic quantity that is the That is, the connection of entropy with information works both ways;. Physical View of Entropy: Physically, Entropy is a disorder of a system and surrounding. Why does entropy have an inverse relation with temperature?. 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. Thermodynamics & Heat: Entropy

Temperature is a derivative of entropy, so temperature is in the mind. Second Law Trickery With perfect knowledge of a system, it is possible to extract all of its energy as work. EY states it clearly: Someone who doesn't know the state of the water will observe a violation of the second law. Let that sink in for a minute. A physical system always has more macroscopic degrees of freedom beyond what we control or observe, and by manipulating them a trickster can always make us see an apparent violation of the second law.

Any attempt to write a stronger law than this will put one at the mercy of a trickster, who can produce a violation of it. But recognizing this should increase rather than decrease our con fidence in the future of the second law, because it means that if an experimenter ever sees an apparent violation, then instead of issuing a sensational announcement, it will be more prudent to search for that unobserved degree of freedom.

That is, the connection of entropy with information works both ways; seeing an apparent decrease of entropy signi fies ignorance of what were the relevant macrovariables.

The Relationship between Entropy and Temperature –

Homework I've actually given you enough information on statistical mechanics to calculate an interesting system. Say you have N particles, each fixed in place to a lattice. Calculate and plot the entropy if you know the total energy: S Eand then the energy as a function of temperature: This is essentially a combinatorics problem, and you may assume that N is large, so use Stirling's approximation.

What you will discover should make sense using the correct definitions of entropy and temperature. Historically, the classical thermodynamics definition developed first. In the classical thermodynamics viewpoint, the system is composed of very large numbers of constituents atoms, molecules and the state of the system is described by the average thermodynamic properties of those constituents; the details of the system's constituents are not directly considered, but their behavior is described by macroscopically averaged properties, e.

The early classical definition of the properties of the system assumed equilibrium. The classical thermodynamic definition of entropy has more recently been extended into the area of non-equilibrium thermodynamics. Later, the thermodynamic properties, including entropy, were given an alternative definition in terms of the statistics of the motions of the microscopic constituents of a system — modeled at first classically, e.

relationship between entropy and temperature

Newtonian particles constituting a gas, and later quantum-mechanically photons, phononsspins, etc. 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.

relationship between entropy and temperature

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.

The Relationship between Entropy and Temperature

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.

relationship between entropy and temperature

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.