# The difference between the entropy and the heat capacity? they are very similar

1. Apr 21, 2011

### su214

the difference between the entropy and the heat capacity? they are very similar!!

hello ...
as we all know that
specific heat capacity = joule/ k
entropy = joule/k
they are same in units

Q= m Cv dT

Q/dT=m Cv................1
dS= dQ/T .....2
from 1 & 2

dS= m Cv ..............??????????????????????????…
i'm now confused ,,entropy can't equal mCv i know i'm wrong ,,but don't know why? and in the same time what does it mean that they have the same units ?

and if entropy measuers the chaos in the system and the specific heat capacity is the amount of heat to raise one Kg of the matter one degree of tempreture
aren't the entropy and the heat capacity related somehow ?

2. Apr 22, 2011

### Mapes

Re: the difference between the entropy and the heat capacity? they are very similar!!

Sure, the heat capacity for a given constraint X (like constant volume or constant pressure) is defined as $C_X=T(\partial S/\partial T)_X$. In your derivation, dQ/T doesn't equal Q/dT, so this can't be used to show that entropy is the same as heat capacity. And it doesn't mean anything that they have the same units; work, heat, and torque are fundamentally different parameters that also share the same units (N-m), for example.

3. Apr 22, 2011

### SteamKing

Staff Emeritus
Re: the difference between the entropy and the heat capacity? they are very similar!!

You all have confused entropy with enthalpy. Enthalpy is a measure of the total heat content of a substance. Entropy is a much more subtle concept, and its description and use form the basis for the Second Law of Thermodynamics.

4. Apr 22, 2011

### Mapes

Re: the difference between the entropy and the heat capacity? they are very similar!!

Who is the "all" you're addressing? Nobody is discussing enthalpy.

5. Apr 22, 2011

### Curl

Re: the difference between the entropy and the heat capacity? they are very similar!!

Son, please. Do not give wrong information on here.

It means nothing.

Also, manipulating some symbols doesn't really give any insight into what entropy is. Actually, the "engineering thermo" education will never explain what entropy or temperature are. For that you have to study on your own

http://en.wikipedia.org/wiki/Entropy_(statistical_thermodynamics)

6. Apr 22, 2011

### SteamKing

Staff Emeritus
Re: the difference between the entropy and the heat capacity? they are very similar!!

If you still think you have not confused enthalpy with entropy, check out the following link:
http://en.wikipedia.org/wiki/Enthalpy

And, Curl, I'm not your son.

7. Apr 23, 2011

### Mapes

Re: the difference between the entropy and the heat capacity? they are very similar!!

It's not clear what you're talking about. What statement do you have a problem with, and how would you revise it?

8. Apr 29, 2011

### jonsayago

Re: the difference between the entropy and the heat capacity? they are very similar!!

I think is a good question. The Fourier law you started: Q= m Cv dT, I think is missing a dot over the Q which means is the heat flux (derivate with respect to time). The heat capacity has a subindex V which means it is a process at constant volume. However, it would still be valid to say:

Q = mCT (1)

Notice Q (without point) refers just to the internal energy in the system, C would be the heat capacity -without specifying if is at constant pressure or volume- and of course, m stands for mass and T for temperature (the units of temperature should be consistent with those of C and should be in kelvin units to make the relationship with entropy concept).

From Eq. (1) it can find out Q/T= mC = entropy

In my opinion is correct, entropy can be deducted from mC, considering C is not a constant anymore, but a parameter that changes with respect to volume and pressure. However, remember that entropy itself is not useful, instead we always find out the change of entropy (dS) from one state to another. This is the reason why I mentioned before that in order to make a comparison with entropy we should use kelvin temperature units.

So entropy can be seen as a disorder parameter, or the capacity to store energy of each component of a system of mass m.

9. Apr 29, 2011

### Mapes

Re: the difference between the entropy and the heat capacity? they are very similar!!

Hi jonsayago, welcome to PF, but please note that personal theories are not appropriate here; your posts should be based on consensus physics.

No, this would make the units inconsistent. dQ is measured in Joules, so that dQ = mcVdT has units [J] = [kg][J/kg/°C][°C]. Note that in this equation, dQ must be an infinitesimal quantity to match dT.

No. If you integrate dQ = mcdT, you get Q = mcΔT, which is different.

Eq. (1) is not correct, so this does not hold.

10. Apr 29, 2011

### jonsayago

Re: the difference between the entropy and the heat capacity? they are very similar!!

First comment I accept Q shouldn't be a derivative with respect to time. It is simply the change with respect to one state and another.
However, Ec. (1) stands under equilibrium conditions. I mean in just one state. The rest of my derivation should be fine.

11. Apr 29, 2011

### jonsayago

Re: the difference between the entropy and the heat capacity? they are very similar!!

"No. If you integrate dQ = mcdT, you get Q = mcΔT, which is different"

How did you integrate this??? I am sure you did a mistake here.

12. Apr 29, 2011

### Mapes

Re: the difference between the entropy and the heat capacity? they are very similar!!

$$\int dQ=\int_{U_1}^{U_2}dU=\int_{T_1}^{T_2}mc_VdT$$

$$\Delta U = Q=mc_V\Delta T$$

where ΔU=U2-U1 is the difference in energy due to the addition of thermal energy Q at constant volume, and where ΔT=T2-T1 is the temperature difference. See http://books.google.com/books?id=8l...=onepage&q=q "heat capacity" m cv ΔT&f=false" for the integrated version, for example. What other way is there to integrate it?

Last edited by a moderator: Apr 25, 2017
13. Apr 29, 2011

### jonsayago

Re: the difference between the entropy and the heat capacity? they are very similar!!

You evaluated the right part of the integral (from T1 to T2) and not left part... You have to evaluate left part too from Q1 to Q2. Someone else out there to comment???

14. Apr 29, 2011

### jonsayago

Re: the difference between the entropy and the heat capacity? they are very similar!!

By the way which software you use to write equations?

15. Apr 29, 2011

### Mapes

Re: the difference between the entropy and the heat capacity? they are very similar!!

dQ is not an exact differential, and there is no such thing as Q1 or Q2. (A state can have an associated energy U or an associated temperature T, but not an associated heat Q; heat describes a path-dependent transfer of energy between two states.) See equation 15.11 http://books.google.com/books?id=8s...ok_result&ct=result&resnum=2&ved=0CDAQ6AEwAQ", for example, where in this case the work W is zero because of the constant-volume constraint.

If you think I'm wrong, please show a reference from the literature.

Last edited by a moderator: Apr 25, 2017
16. Apr 29, 2011

### Mapes

Re: the difference between the entropy and the heat capacity? they are very similar!!

You can enclose your equations between {tex} and {/tex}, using straight brackets instead of curly brackets. Or use {itex} and {/itex} for inline equations (within a paragraph). Click on anyone's equation to get a popup window showing their code.

17. Apr 29, 2011

### jonsayago

Re: the difference between the entropy and the heat capacity? they are very similar!!

Here is the importance of using the absolute scale (kelvin) for temperature. When using it Q = U. Eq 33.4 of

Though Q is not a state variable, the entropy S is a state variable (Dunod, Physique statistique). So we could have divided both sides of the equation by T first and then integrate from one state to another.
Check the entropy section of the book you quoted.

18. Apr 29, 2011

### jonsayago

Re: the difference between the entropy and the heat capacity? they are very similar!!

By the way don't forget to tell me which program you use to set up equations in the internet!!!

19. Apr 29, 2011

### Mapes

Re: the difference between the entropy and the heat capacity? they are very similar!!

I don't see the equation Q = mCT anywhere. I only see Q = mcVΔT. Meaning that when you heat a system at constant volume, adding energy Q, the temperature change is ΔT = Q/(mcV).

So far you've not shown any evidence from the literature that S = mC, as you claim.

On the typesetting: see my post #16.

20. Apr 29, 2011

### Mapes

Re: the difference between the entropy and the heat capacity? they are very similar!!

OK, I had a minute and worked this through:

$$dQ=mc_VdT$$

Divide by T:

$$\frac{dQ_\mathrm{rev}}{T}=dS=mc_V\frac{dT}{T}$$

Integrate:

$$\int_{S_1}^{S_2}dS=\int_{T_1}^{T_2}mc_V\frac{dT}{T}$$

$$S_2-S_1=\Delta S=mc_V\ln\left(\frac{T_2}{T_1}\right)$$

This is not even close to S=mC.