Effect of temperature on Entropy

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Discussion Overview

The discussion revolves around the relationship between temperature and entropy, particularly focusing on how changes in temperature affect entropy in thermodynamic systems. Participants explore the implications of the equation dS = dQ / T and its interpretations in various contexts, including reversible processes and energy input scenarios.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant notes that as temperature increases, entropy also increases due to more available energy states, but questions how lower temperatures can lead to greater entropy changes according to the equation.
  • Another participant clarifies that the equation describes an infinitesimal increase in entropy at constant temperature and that the overall change in entropy with increasing temperature is always positive.
  • A different viewpoint suggests that a larger change in entropy occurs at lower temperatures due to the relative increase in randomness when energy is added to a less disordered system.
  • Participants discuss the importance of specifying conditions of energy input and the context of heat exchange when considering entropy changes.
  • One participant provides an analogy comparing the effects of adding energy to systems at different temperatures, suggesting that the initial state of disorder influences the resulting entropy change.
  • Another participant mentions that if both heat additions are reversible, the entropy change in the higher temperature case may be less than that in the lower temperature case, depending on the specifics of the energy input.

Areas of Agreement / Disagreement

Participants express differing views on how temperature affects entropy changes, particularly regarding the implications of the dS = dQ / T equation and the conditions under which entropy changes occur. There is no consensus on the interpretations presented.

Contextual Notes

Participants highlight the need for clarity regarding the conditions of energy input and the assumptions underlying the equations used, indicating that the discussion is nuanced and context-dependent.

Who May Find This Useful

This discussion may be useful for students and individuals interested in thermodynamics, particularly those exploring the concepts of entropy and temperature relationships in physical systems.

weng cheong
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i'm a pre-U student, and i came across this when i study the topic on entropy

dS = dQ / T

i understand that as temperature increases, entropy increases as well, as there are more quanta of energy and more thermal states(energy levels) available.

however according to this equation, it seems to indicate that with a lower temperature, we can get a greater entropy?
 
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S is entropy. dS is change in entropy.
So, for a given temperature T, the change in entropy is equal to the change in heat energy divided by whatever the temperature that system is currently in.
 
The equation you wrote describes the infinitesimal increase in entropy of a system at constant temperature when infinitesimal energy is added reversibly by heating. That's not the same as the change in entropy of a system with increasing temperature, which is \partial S/\partial T. This quantity is, indeed, always positive.

You can integrate your equation to get \Delta S=Q\ln(T_2/T_1), which confirms that entropy increases with temperature when a system is heated.

Does this make sense?
 
You get a larger change in entropy, that's correct.

ETA - I figured that constant temperature and reversibility were givens, considering the Clausius formalism used by the OP. (Although that dQ should be dQrev, which is how I recall seeing it written in textbooks.)

ETA 2 - One analogy that might be useful - if you scream at a sports game (add a tiny bit of energy to a high-temperature system), most likely you will not make that much of a dent in the general soundscape (a small change in entropy). If you yell in the middle of a wedding (adding a tiny bit of energy to a low-temperature system), it would be far more dramatic (a large change in entropy).
 
Last edited:


So, for a given temperature T, the change in entropy is equal to the change in heat energy divided by whatever the temperature that system is currently in.

Careful!

The temperature of the the system at the point (moment) of heat exchange, currently is a bit vague and could mean after the exchange.

Note also it is a differential relationship so may be integrated from point to point.
 
Imagine this situation.
You provide X joules of heat to a system at
1)say 100 K and 2)say 300K

So, in the first case, what you will observe is the there will be a larger change in the randomness than in the second case, as due to the pre-existing higher temperature, there will be already a large amount of disorder in the system!

It's just like shuffling a deck of kinda properly arranged cards (analogous to a lower T) will give you a larger change in disorder than shuffling a pack of cards that are already random in order (higher temperature!).

Am I correct?
 
Imagine this situation.
You provide X joules of heat to a system at
1)say 100 K and 2)say 300K

The entropy change in the system, in both cases, depends upon the conditions of energy input, which have not been specified.
 
Studiot said:
The entropy change in the system, in both cases, depends upon the conditions of energy input, which have not been specified.

and can you please help me out wit what that is? :)
 
If both additions of heat are reversible then the entropy change of the second case input is 1/3 of the first.

The addition of heat may become the work of expansion, which allows greater entropy in the form of freedom of space to occupy,

or

It may be taken up in a phase (state) change so the particles become more disordered.
 

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