cotkhd
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#1
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#1
I understand that entropy is the amount of disorder in a system, and that gaseous systems have larger entropies BUT

The units for entropy are Joules/Kelvin or Joules/Kelvin*mol

What do these units actually mean?
Like if you have an object moving at 3m/s, we know that it goes 3 meters in 1 second...applying the same thought to the units of entropy, what do the units of entropy mean?
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MexicanKeith
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(Original post by cotkhd)
I understand that entropy is the amount of disorder in a system, and that gaseous systems have larger entropies BUT

The units for entropy are Joules/Kelvin or Joules/Kelvin*mol

What do these units actually mean?
Like if you have an object moving at 3m/s, we know that it goes 3 meters in 1 second...applying the same thought to the units of entropy, what do the units of entropy mean?
This is actually quite a difficult question to answer well.

I'll have a go at explaining how we might begin to understand the units of entropy and why they make sense.

First of all, it is simplest if we consider the entropy change associated with some process.

For some process (eg boiling water) occurring at a constant temperature the change in entropy can be defined as the (heat) energy gained by the system divided by the temperature at which the process occurs. Or, in symbols

ΔS = ΔQ/T

ΔQ has units of Joules, T has units of Kelvin, hence we get the unit of ΔS as Joule/Kelvin

I can't offer the same obvious physical interpretation as with your speed analogy, but I can offer an argument as to why this unit makes sense.

Firstly, relating to ΔQ, it makes physical sense that, if something has more energy, it is more disordered. Think of a flag, if there isn't much wind, it will sit in one place, very orderly! But if the wind picks up it will flap around through all sorts of different arrangements and these different possible arrangements in space associated with more energy give the flag a greater entropy.

So entropy being proportional to energy in some way makes sense.

The inverse relationship with temperature also makes sense, but its harder to get your head around.

basically it means, if a process happens at a low temperature it causes a big entropy increase, but if the same process happens at a high temperature, the entropy increase is smaller.

The way I think about this is the way Peter Atkins explains it.
A sneeze in a busy street causes very little disruption (ie a process occurring at high temperature cause little entropy increase)
But the same sneeze in a quiet library would cause lots of disruption (ie a process occurring at low temperature causes a bigger entropy increase).

So hopefully that gives you at least some incite into the meaning of the units of entropy.

I can't think of any simpler way to think about the units of entropy sadly.


Another interesting point to consider:
Heat capacity also has the units Joules/Kelvin, and in this instance it has a much simpler interpretation. Here the heat capacity is simply the amount of energy required to raise the temperature by 1 kelvin. This simple explanation however, doesn't work for entropy!
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cotkhd
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#3
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#3
(Original post by MexicanKeith)
This is actually quite a difficult question to answer well.

I'll have a go at explaining how we might begin to understand the units of entropy and why they make sense.

First of all, it is simplest if we consider the entropy change associated with some process.

For some process (eg boiling water) occurring at a constant temperature the change in entropy can be defined as the (heat) energy gained by the system divided by the temperature at which the process occurs. Or, in symbols

ΔS = ΔQ/T

ΔQ has units of Joules, T has units of Kelvin, hence we get the unit of ΔS as Joule/Kelvin

I can't offer the same obvious physical interpretation as with your speed analogy, but I can offer an argument as to why this unit makes sense.

Firstly, relating to ΔQ, it makes physical sense that, if something has more energy, it is more disordered. Think of a flag, if there isn't much wind, it will sit in one place, very orderly! But if the wind picks up it will flap around through all sorts of different arrangements and these different possible arrangements in space associated with more energy give the flag a greater entropy.

So entropy being proportional to energy in some way makes sense.

The inverse relationship with temperature also makes sense, but its harder to get your head around.

basically it means, if a process happens at a low temperature it causes a big entropy increase, but if the same process happens at a high temperature, the entropy increase is smaller.

The way I think about this is the way Peter Atkins explains it.
A sneeze in a busy street causes very little disruption (ie a process occurring at high temperature cause little entropy increase)
But the same sneeze in a quiet library would cause lots of disruption (ie a process occurring at low temperature causes a bigger entropy increase).

So hopefully that gives you at least some incite into the meaning of the units of entropy.

I can't think of any simpler way to think about the units of entropy sadly.


Another interesting point to consider:
Heat capacity also has the units Joules/Kelvin, and in this instance it has a much simpler interpretation. Here the heat capacity is simply the amount of energy required to raise the temperature by 1 kelvin. This simple explanation however, doesn't work for entropy!
Thank you so much!!!
Referring to ''if a process happens at a high temperature, the entropy increase is smaller''- it seems to me that this is because given bodies already are energetically excited and so have a large entropy prior to the future reaction (which would induce a small entropy change)? Is that correct?

Thank you for your response! A level chem just got easier thanks to you
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MexicanKeith
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#4
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#4
(Original post by cotkhd)
Thank you so much!!!
Referring to ''if a process happens at a high temperature, the entropy increase is smaller''- it seems to me that this is because given bodies already are energetically excited and so have a large entropy prior to the future reaction (which would induce a small entropy change)? Is that correct?

Thank you for your response! A level chem just got easier thanks to you
That's the way to think of it. At high Temperature there is already significant disorder so one small change doesn't make much difference, but at low T there is very little disorder so the small change is much more significant! exactly as you say

I will point out, you really don't need a high level of understanding of entropy for A levels. It's quite a complicated quantity and so you only discuss it briefly at A level usually
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cotkhd
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#5
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#5
(Original post by MexicanKeith)
That's the way to think of it. At high Temperature there is already significant disorder so one small change doesn't make much difference, but at low T there is very little disorder so the small change is much more significant! exactly as you say

I will point out, you really don't need a high level of understanding of entropy for A levels. It's quite a complicated quantity and so you only discuss it briefly at A level usually
Thanks man. My teachers tell me the same thing about difficult concepts but for me I really need to understand processes and the reasons of ''why'' and ''how'' to remember it really well
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MexicanKeith
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#6
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#6
(Original post by cotkhd)
Thanks man. My teachers tell me the same thing about difficult concepts but for me I really need to understand processes and the reasons of ''why'' and ''how'' to remember it really well
Fair enough
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