The enthalpy, H, is the heat content of the system, and so the change in enthalpy, H, is the change in heat content of the system. For the mathematician the problem of communication is of finding the most efficient way of mapping text messages to streams of bits.
The macrostate variable, temperature, is recognized as an expression of the average of the microstate variables, an average kinetic energy for the system. The thing to note is that the massage is made up of letters from the alphabet but what is transmitted down the communication line are only dots and dashes.
If I have a text message of characters what is the smallest number of bits I need to transmit down the line? We are free in our mental accounting to consider them as two separate systems or as two non-interacting parts of a single system.
Let E be an encoding function that maps messages from A to messages from B. And also keep in mind that "order" is a subjective term, and as such it is subject to the whims of interpretation. Entropy is also sometimes confused with complexity, the idea being that a more complex system must have a higher entropy.
Entropy adds, as it should!
The W is the number of microstates in the macrostate in question. So in one sense, the logarithm is there because that what makes the math work out right and matches observation.
Also entropy is all about measure and not random variable. The easiest answer to the question, "What is entropy?
We all would like to learn: To reconcile the multiplicative permutations of the number of microstates W with the desired additive property of a state variable Swe must have S proportional to log W. However, if F is positive, such that H is greater than T S, then the reaction will not happen spontaneously; we still need at least F worth of energy to make it happen.
Logs are very helpful in many areas, especially when you are dealing with a very large span of sizes, because it compresses it down to something manageable. This was an early insight into the second law of thermodynamics. So put the containers together and remove a partition. Whenever you multiply two integers, the numbers of their respective digits add.
When two identical gases are mixed, the entropy is additive, as I wrote, because the gas atoms are indistinguishable. Quantum mechanics has its own, peculiar rules for doing that, but they are not relevant to the fundamental definition of entropy.
Morse code maps letters to dots and dashes. Gas atoms are indistinguishable, so the system looks just as when the containers were separated. When I attempt my own examples, the majority of them fail to conform to it.
Contrary to the definition seen in equation 1neither the temperature nor the heat energy appear explicitly in this equation. For example, imagine a black box whose observable properties temperature, pressure, etc. Let us dispense with at least one popular myth: The quantum mechanical definition of entropy is identical to that given for statistical mechanics, in equation 6.
The length of the encoding will be proportional to the length of the message. In that case the entropy is a measure of the probability for a givem macrostate, so that a high entropy indicates a high probability state, and a low entropy indicates a low probability state equation 6.
So why use a logarithm? In the hands of Clausius and his contemporarys, entropy was an important, but strictly thermodynamic property. A reversible process is one that does not deviate from thermodynamic equilibrium, while producing the maximum work.Entropy Formula Entropy is a measure how much the energy of atoms and molecules become more spread out in a process and can be defined in terms of statistical probabilities of a system or in terms of the other thermodynamic quantities.
Intuitive explanation of entropy. Ask Question. up vote 94 down vote favorite. we should start with an intuitive concept and try to define a mathematical formula satisfying the properties we want it to satisfy in the informal sense.
So 'informal' answers are the most formal. Let's be explicit here and write down the full expression. Write a mathematical formula that includes entropy. Explain each of the terms in the formula. Lab 10 Entropy Introduction: Connecting Your Learning Write a mathematical formula that includes entropy.
Explain each of the terms in the formula.
Lab Report. write clearly is as important a mathematical skill as being able to solve equations. Mastering the ability to write clear mathematical explanations is important for formula on a line of its own. It’s hard to pick out the important formulas below: If dis Bob’s distance above the ground in feet, thend.
Answer to Write a mathematical formula that includes entropy. Explain each of the terms in the formula. Jul 30, · Help me Understand Boltzmann's entropy formula: S = k log W? Big community funding update!
You can help! Ask MetaFilter querying the hive mind For a mathematical treatment, You can write down large numbers.Download