# Entropy

Hi everyone, does anyone have an enlightening definition for entropy rather then tendency to caos/randomness or function of E+PV??
Original post by _Simo_
Hi everyone, does anyone have an enlightening definition for entropy rather then tendency to caos/randomness or function of E+PV??

The tendency to chaos/randomness is a rather poor definition of entropy as entropy is more to do with the unavailability of thermal energy for the conversion to mechanical energy.

Strictly, you could say the following equation defines entropy elegantly enough:

S = k ln(W) *

*note that older texts express this as S = k log(W)

Where S is the entropy, k is Boltzmann’s constant (1.380649 x 10^-23 J K^-1) and W is the number of configurations/states of the particles in the sample (i.e a property largely dependent on the energies of the particles).
So does this unavailability of thermal energy decrease the greater the entropy gets?
or it is just the possibility to convert it in to mechanical energy?
It sounds very connected with enthalpy then or they are completely independent?
And does W represent the poorly defined by my old teacher randomness then?

cheers, i really appreciate your help, this entropy makes my head spin, because in Chemistry they need it to predict reactions along with the enthalpy, but they don't want to spend too much time to actually explain what it is!! Very annoying.
(edited 1 year ago)
Someone double check this but the way I understand how entropy is related to the unavailability of thermal energy is to understand how it entropy is related to useful work.

The unavailability of thermal energy is directly related to the possibility to convert it into mechanical energy.

As you probably know systems that tend towards disorder, and the more disordered a system is the less work it can do, e.g. burning coal into carbon dioxide.

Enthalpy is the heat energy/thermal energy in a thermodynamic system so they are related as this energy can be used to do useful work.
Original post by _Simo_
So does this unavailability of thermal energy decrease the greater the entropy gets?
or it is just the possibility to convert it in to mechanical energy?
It sounds very connected with enthalpy then or they are completely independent?
And does W represent the poorly defined by my old teacher randomness then?

cheers, i really appreciate your help, this entropy makes my head spin, because in Chemistry they need it to predict reactions along with the enthalpy, but they don't want to spend too much time to actually explain what it is!! Very annoying.

Entropy is a weird one indeed and I can’t say I understand it especially well. I’ve just finished my A levels having only done some very basic thermodynamics, which isn’t too enlightening.

Entropy increases with temperature (this is sourced by Chemical Structure and Reactivity by Wothers and Keeler). This to me would imply that it’s the possibility to convert it to mechanical energy, as eventually you’ve got so much extra thermal energy that only a fraction actually gets converted usefully. Take this with a pinch of salt though, as I’m probably wrong.

Both enthalpy and entropy are thermodynamic quantities that to some extent, are connected. Their definitions more or less support this:

-Enthalpy is the thermal energy change brought about by a process under a constant pressure.

-Entropy is the thermal energy unavailable to convert to mechanical (or useful) energy per kelvin. There are three particularly important entropy changes in chemical thermodynamics, one such entropy change is ΔS(surroundings), which is defined by the expression -ΔH/T, where ΔH is the enthalpy change and T is the temperature in K.

Hence, ΔG = ΔH - TΔS(system)

Mathematically, it can also be shown that both ΔG = -TΔS(total) and ΔG = -T(ΔS(system) + ΔS(surroundings)) are valid expressions.

You could say W is the so called randomness, but it’s actually more to do with the distribution of the energies within a substance.

A system will have discrete energy levels within it, so the molecules inside can only hold specific amounts of energy, in part due to the fact the system itself has a finite amount of internal energy to distribute.

In a simple (but unrealistic) example, let’s say we have 5 energy levels (excluding ε0, the energy level with 0 associated energy) and 14 molecules in the system. One way we could arrange these 14 molecules is to have 8 of them on ε0, 3 on ε1, 2 on ε2, 1 on ε3 and none on ε4 and ε5.

The total thermal energy of the system is given by the sum of the energies associated with each energy level times the number of molecules on said energy level, so if we say each energy level has 1 unit of energy more than the last, the total energy is 8(0) + 3(1) + 2(2) + 1(3) + 0(4) + 0(5) = 10 units. At a single given temperature, this distribution will be more likely than at any other temperature, as the energy supplied can only be 10 units at one particular temperature.

W is the number of ways we could feasibly attain this particular distribution. It is given by the expression W = (N!)/(n0! x n1! x n2! x …), where N is the number of molecules, n0 is the number of molecules on energy level 0, n1 is the number of molecules on energy level 1 and so on. In this case, W = (14!)/(8! x 3! x 2! x 1! x 0! x 0!) = 1.8018 x 10^5 ways.

We can also calculate S: 1.380649 x 10^-23 J K^-1 x ln(1.8018 x 10^5) 1.67 x 10^-22 J K^-1

Hence the molar entropy is ‘1.67 x 10^-22 J K^-1’ x 6.02214076 x 10^23 mol^-1 +100.6 J K^-1 mol^-1
(edited 1 year ago)
Original post by D_Rkman
Someone double check this but the way I understand how entropy is related to the unavailability of thermal energy is to understand how it entropy is related to useful work.

The unavailability of thermal energy is directly related to the possibility to convert it into mechanical energy.

As you probably know systems that tend towards disorder, and the more disordered a system is the less work it can do, e.g. burning coal into carbon dioxide.

Enthalpy is the heat energy/thermal energy in a thermodynamic system so they are related as this energy can be used to do useful work.

This was literally posted as I was typing my response to the OP.

It does look like a good interpretation and actually this part “As you probably know systems that tend towards disorder, and the more disordered a system is the less work it can do, e.g. burning coal into carbon dioxide.” really helps as I was honestly trying to work out why entropy increases with temperature with regards to work done. I guess I was overlooking the fact that the distribution is less skewed towards lower energies at higher temperatures, so thanks so much for helping me realise the error of my ways!

My only criticism of your post is the definition of enthalpy, as you haven’t stated this relies on a constant pressure. Strictly with that definition, you could also be talking about internal energy, which is the thermal energy in a thermodynamic system at constant volume.
Thanks for all the amazing replies.

To make it simple for my brain and see if i have understood, if I have a close system like an air ballon, the molecules inside will have an internal energy called Enthalpy, they will be subjected to changes in the energy at constant pressure called ΔH. Only some of this internal energy will not be available to do work depending on the Entropy, which depends on W or the probability of the distribution of the particles in the different energy levels of the system. For a practical maybe stupid example, if a particle will have too much kinetic energy the system will not be able to harness that energy to convert it in to mechanical work.
So the Entropy defines how much Enthalpy can be used for i.e. a chemical reaction.

Although i know i don't really need to know all this things and I just need to remember the formula, I thank you again for the help as, I only learn if I understand.
Original post by _Simo_
Thanks for all the amazing replies.

To make it simple for my brain and see if i have understood, if I have a close system like an air ballon, the molecules inside will have an internal energy called Enthalpy, they will be subjected to changes in the energy at constant pressure called ΔH. Only some of this internal energy will not be available to do work depending on the Entropy, which depends on W or the probability of the distribution of the particles in the different energy levels of the system. For a practical maybe stupid example, if a particle will have too much kinetic energy the system will not be able to harness that energy to convert it in to mechanical work.
So the Entropy defines how much Enthalpy can be used for i.e. a chemical reaction.

Although i know i don't really need to know all this things and I just need to remember the formula, I thank you again for the help as, I only learn if I understand.

In a balloon under a constant temperature it is reasonable to assume that the thermal energy, volume and pressure are all constant, hence both the enthalpy and internal energy will be equal.

You will get a change in the thermal energy of the balloon if you change the temperature, but the change in the internal energy will not be ΔH, as this would alter the volume (thus internal energy by definition cannot be measured) and the gas would expand or contract, altering the pressure (thus enthalpy by definition cannot be measured).

The rest of your response appears to be bang-on, so you’ve clearly got most of it.

Btw what level are you studying for? The book I quoted was undergraduate level, so if you are at that level, you probably ought to understand entropy conceptually and perhaps in more detail than I attempted to explain.
(edited 1 year ago)
Ok, i clearly choose the wrong example then! sorry...

I'm studying for A levels Chemistry, but Enthalpy and Entropy is a topic that always fascinated me and teachers always try to escape from explaining it! It is quite hard to figure them visually, it's quite up in the air, not really associable to everyday life. But I will digest them some how.

What undergraduate course are you following??
Original post by _Simo_
Ok, i clearly choose the wrong example then! sorry...

I'm studying for A levels Chemistry, but Enthalpy and Entropy is a topic that always fascinated me and teachers always try to escape from explaining it! It is quite hard to figure them visually, it's quite up in the air, not really associable to everyday life. But I will digest them some how.

What undergraduate course are you following??

Nah don’t apologise. You’ve done very well to understand a uni level concept as well as you have. It’s also good to see someone actually read up on things they find interesting.

I’ll be looking at studying MChem chemistry (hopefully at Oxford) after my gap year.

Hbu?
Gap years are the best! I'm actually a perfect example of a very long gap year! I've done my studies in italy and started uni, then decided to have a gap year where I traveled around the world, it has been a many years gap year actually, now I want to go back to uni but to enter I need Chem and Biology A levels, so I'm happily back on the books. But Physics has always been a great passion!
I hope you will manage to enter Oxford! Sounds like you can become someone if you want over there....
Original post by _Simo_
Gap years are the best! I'm actually a perfect example of a very long gap year! I've done my studies in italy and started uni, then decided to have a gap year where I traveled around the world, it has been a many years gap year actually, now I want to go back to uni but to enter I need Chem and Biology A levels, so I'm happily back on the books. But Physics has always been a great passion!
I hope you will manage to enter Oxford! Sounds like you can become someone if you want over there....

Thanks for the kind words. I hope the studies go well on your end as well.

Need any resources for A level chemistry? I didn’t do biology, so I can’t really offer much for that.
Original post by TypicalNerd
Thanks for the kind words. I hope the studies go well on your end as well.

Need any resources for A level chemistry? I didn’t do biology, so I can’t really offer much for that.

to be honest I'd really appreciate if you could advise a book, the one they provide here is more of a gcse book and the notes are undergraduate level!! there is a big gap between the two. Thanks man!
Original post by _Simo_
to be honest I'd really appreciate if you could advise a book, the one they provide here is more of a gcse book and the notes are undergraduate level!! there is a big gap between the two. Thanks man!

In terms of books, it depends on the exam board you are doing, really. Hodder education makes some good ones for all the UK exam boards.

In terms of online resources…

General resources:

PMT (notes and topic specific questions): https://www.physicsandmathstutor.com

Study Mind: https://studymind.co.uk

Plutonium science: https://plutoniumscience.com

Chemistry resources:

The Exam Formula (my favoured source of past papers): https://www.theexamformula.co.uk/

Dr Clay (Website): https://drclays-alevelchemistry.com/

Original post by _Simo_
to be honest I'd really appreciate if you could advise a book, the one they provide here is more of a gcse book and the notes are undergraduate level!! there is a big gap between the two. Thanks man!

You can access Hodder education’s science books here:

https://www.hoddereducation.co.uk/science

In the filters, ‘exam’ represents the exam board and I’d also set the level to 16 - 18.

Hopefully they aren’t too extortionate!
Original post by _Simo_
to be honest I'd really appreciate if you could advise a book, the one they provide here is more of a gcse book and the notes are undergraduate level!! there is a big gap between the two. Thanks man!

You could also try: www.ibchem.com
and its YouTube channel: Colourful Solutions

Here's a video about entropy for example:
(edited 1 year ago)
Super Guys! Thank you so much @TypicalNerd and @charco. I hope to catch you around for more fun chats in the future! Thanks for your help!