Is there a relationship between \Delta H_{sys} and \Delta S_{surroundings}?

Click For Summary

Discussion Overview

The discussion revolves around the relationship between the change in enthalpy (\Delta H_{sys}) and the change in entropy of the surroundings (\Delta S_{surroundings}) in the context of thermodynamics, particularly focusing on spontaneous processes and the implications of the second law of thermodynamics.

Discussion Character

  • Debate/contested
  • Technical explanation
  • Conceptual clarification

Main Points Raised

  • Some participants assert that a spontaneous process is likely to occur if \Delta S > 0, referencing the second law of thermodynamics.
  • One participant questions the calculation of \Delta S, noting the absence of specific entropy values (S_{1} and S_{2}).
  • Another participant explains that if \Delta H < 0, enthalpy is released from the system, suggesting that this could lead to a decrease in entropy, which raises questions about the consistency with Gibbs energy.
  • Some participants argue that if the system is not isolated and experiences a decrease in enthalpy, the surroundings absorb energy, leading to an overall increase in entropy, thus aligning with the second law.
  • One participant mentions that it is possible to calculate \Delta S_{surroundings} if \Delta H_{sys} is known, proposing a proportionality under certain conditions, such as constant volume.
  • Another participant provides a counterexample using water, stating that cooling it results in a decrease in entropy, yet the total entropy increases due to the surroundings warming up.

Areas of Agreement / Disagreement

Participants express differing views on the relationship between \Delta H_{sys} and \Delta S_{surroundings}, with some suggesting a direct proportionality under specific conditions, while others challenge this notion with examples that illustrate complexities in the relationship. The discussion remains unresolved regarding the exact nature of this relationship.

Contextual Notes

There are limitations in the assumptions made regarding the conditions under which enthalpy and entropy changes are related, particularly concerning the definitions of isolated versus non-isolated systems and the implications of work performed on the system.

erty
Messages
26
Reaction score
0
According to the 2nd law of thermodynamics, a spontaneous process will occur (or rather: is very likely to occur) if \Delta S &gt; 0.

A chemical process occurs if \Delta G &lt; 0, where G = H - TS.

Example:
H = -100 kJ
T = 1 K
S = -10 kJ/K
so \Delta G = - 190 kJ. In this example, \Delta G &lt; 0 but \Delta S &lt; 0.
Doesn't this contradict the 2nd law?
 
Science news on Phys.org
I don't see an S_{1} and an S_{2} so how did you compute \Delta S ?

Daniel.
 
dextercioby said:
I don't see an S_{1} and an S_{2} so how did you compute \Delta S ?

Daniel.

Okay, then
\Delta H = -100 \mbox{kJ}
T = 1 \mbox{K} and
\Delta S = -10 \mbox{kJ/K}
because \Delta G = \Delta H - T\Delta S where T is constant.
 
erty said:
Okay, then
\Delta H = -100 \mbox{kJ}
T = 1 \mbox{K} and
\Delta S = -10 \mbox{kJ/K}
because \Delta G = \Delta H - T\Delta S where T is constant.

If H changes, then that means that the system is not left to itself but is externally acted upon. So we are not dealing with a spontaneous process.
 
vanesch said:
If H changes, then that means that the system is not left to itself but is externally acted upon. So we are not dealing with a spontaneous process.

If \Delta H &lt; 0, then enthalpy is released from the system to the surroundings. It would make sense, if I had to add enthalpy (\Delta H &gt; 0, \qquad H = U + pV) and the entropy decreased, but that's not true according to the Gibbs energy.
 
Last edited:
If the system is isolated, a spontaneous process will increase its entropy. The Universe is an isolated system in itself, so entropy is always increasing.
But if there is a variation in entalpy (a decrease) at constant temperature T, for sure your system is not isolated. The environment is absorbing such energy, increasing its entropy in a greater extent than the entropy lost by the system (the variation, in absolute value, of the entalpy is grater than that of the entropy, as variation og G is negative). So the universe, the system and the environment, experiments an increase in entropy. This is the result of the second law. No contradiction at all.
 
erty said:
If \Delta H &lt; 0, then enthalpy is released from the system to the surroundings. It would make sense, if I had to add enthalpy (\Delta H &gt; 0, \qquad H = U + pV) and the entropy decreased, but that's not true according to the Gibbs energy.

No of course not. Take water. You extract enthalpy (you cool it). It freezes, and its entropy decreases...
 
vivesdn said:
If the system is isolated, a spontaneous process will increase its entropy. The Universe is an isolated system in itself, so entropy is always increasing.
But if there is a variation in entalpy (a decrease) at constant temperature T, for sure your system is not isolated. The environment is absorbing such energy, increasing its entropy in a greater extent than the entropy lost by the system (the variation, in absolute value, of the entalpy is grater than that of the entropy, as variation og G is negative). So the universe, the system and the environment, experiments an increase in entropy. This is the result of the second law. No contradiction at all.

I get it, thanks! \Delta S_{total} &gt; 0, even though \Delta S_{sys} &lt; 0, because \Delta H_{sys} &lt; 0 according to the Gibbs energy and the conditions for a spontaneous process.

Is it possible to calculate the \Delta S_{surroundings}, if I know the \Delta H_{sys}? I mean, is there any proportionality between those two variables?
 
vanesch said:
No of course not. Take water. You extract enthalpy (you cool it). It freezes, and its entropy decreases...

Yes, but the \Delta S_{total} &gt; 0, because the surroundings get warmer.
(Or did I get this wrong?)
 
Last edited:
  • #10
erty said:
Is it possible to calculate the \Delta S_{surroundings}, if I know the \Delta H_{sys}? I mean, is there any proportionality between those two variables?

If my memory is still readable, I would say that \Delta S_{surroundings} is equal to \Delta H_{sys} if volume is constant (more generally, if there is no work performed of PV type). Then \Delta H_{sys} is the thermal energy transferred.
If there is work performed, then enthalpy is not equal to Q, the heat.
 

Similar threads

Undergrad Minimization of the Gibbs energy when number of molecules varies
  • · Replies 16 ·
Replies
16
Views
3K
Chemistry Entropy in isolated composite system for irreversible process
  • · Replies 3 ·
Replies
3
Views
3K
Chemistry Show that book levitation by absorption of heat violates 2nd law
  • · Replies 13 ·
Replies
13
Views
3K
Chemistry How to derive 2nd law extremum principles for U, A, G, and H?
  • · Replies 1 ·
Replies
1
Views
3K
Chemistry A calculation of enthalpy, entropy, and Gibbs energy of vaporization
  • · Replies 1 ·
Replies
1
Views
2K
Graduate What is the second law of thermodynamics
  • · Replies 1 ·
Replies
1
Views
2K
High School Infrared Detectors & The 2nd Law of Thermodynamics
  • · Replies 152 ·
6
Replies
152
Views
11K
Graduate 1st law, 2nd law, entropy by Gyftopoulos / Beretta is confusing
  • · Replies 7 ·
Replies
7
Views
2K
Quantification of Entropy and the 2nd Law of Thermodynamics
  • · Replies 1 ·
Replies
1
Views
1K
Typical question: Entropy of the universe, of surroundings
  • · Replies 3 ·
Replies
3
Views
1K