Intro to thermal Physics - D. V. Schroeder -Entropy question

In summary, increasing temperature correspond to a decreasing slope on Entropy vs Energy graph, which is observed to be an increasing slope too when the system increases in temperature.
  • #1
SebastianRM
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Hey guys, so I am reading this book and on pages 89-90, the author says:
"Increasing temperature correspond to a decreasing slope on Entropy vs Energy graph", then a sample graph is provided, and both in that graph and in the numerical analysis given in page 87 the slope is observed to be an increasing slope too when the system increases in temperature. So I am somewhat confused.
Thank you in advance!
 
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  • #2
SebastianRM said:
Hey guys, so I am reading this book and on pages 89-90, the author says:
"Increasing temperature correspond to a decreasing slope on Entropy vs Energy graph", then a sample graph is provided, and both in that graph and in the numerical analysis given in page 87 the slope is observed to be an increasing slope too when the system increases in temperature. So I am somewhat confused.
Thank you in advance!
Which is the horizontal axis, energy or entropy?
 
  • #3
SebastianRM said:
Hey guys, so I am reading this book and on pages 89-90, the author says:
"Increasing temperature correspond to a decreasing slope on Entropy vs Energy graph", then a sample graph is provided, and both in that graph and in the numerical analysis given in page 87 the slope is observed to be an increasing slope too when the system increases in temperature. So I am somewhat confused.
Thank you in advance!

While the book is well-known, not everyone has it. So, it would have been good to include the graph you mention.
upload_2019-2-23_1-32-47.png

The horizontal axis running left-to-right [the lower axis] is the energy-count [itex]q_A[/itex] in the A-EinsteinSolid (where the energy is [itex]U_A=q_Ahf[/itex]).
The horizontal axis running right-to-left [the upper axis] is the energy-count [itex]q_B[/itex] in the B-EinsteinSolid, where [itex]q_A+q_B=100[/itex] in this example.

As the energy-count [itex]q_A[/itex] increases (to the right),
the entropy [itex]S_A[/itex] is increasing (so the slope is positive)
but that slope is decreasing [since increments are decreasing]
(so temperature [itex]T_A=\left(\frac{\partial S_A}{\partial U_A}\right)^{-1}[/itex] is increasing).

As energy-count [itex]q_B[/itex] increases (to the left),
the entropy [itex]S_B[/itex] is increasing (so the slope is positive)
but that slope is decreasing [since increments are decreasing]
(so temperature [itex]T_B=\left(\frac{\partial S_B}{\partial U_B}\right)^{-1}[/itex] is increasing).

Given an initial state [itex](q_A,q_B)[/itex], with [itex]q_A+q_B=100[/itex] for the combined system,
the system statistically evolves towards equilibrium (where [itex] S_{total} [/itex] has slope zero).
Here equilibrium is at [itex](q_A,q_B)=(60,40)[/itex].
Since there are many more states near [itex](60,40)[/itex],
if we start at [itex](30,70)[/itex], the system statistically evolves to the right from [itex](30,70)[/itex], and
if we start at [itex](70,30)[/itex], the system statistically evolves to the left from [itex](70,30)[/itex].
 

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1. What is thermal physics and why is it important?

Thermal physics is the branch of physics that studies the behavior of matter at a microscopic level, specifically in relation to temperature and heat. It is important because it helps us understand the fundamental principles behind many everyday phenomena, such as heat transfer, phase changes, and thermodynamics.

2. What is entropy and how does it relate to thermal physics?

Entropy is a measure of the disorder or randomness in a system. In thermal physics, it is closely related to the concept of heat and how it flows from hot to cold objects. The second law of thermodynamics states that the total entropy of a closed system will always increase over time, which is why heat naturally flows from hot to cold objects.

3. How is the concept of entropy used in engineering and technology?

In engineering and technology, the concept of entropy is used to design and improve systems that involve heat transfer, such as refrigerators, engines, and power plants. By understanding how heat flows and how it affects the overall entropy of a system, engineers can create more efficient and effective designs.

4. Can entropy be reversed or decreased?

No, according to the second law of thermodynamics, the total entropy of a closed system will always increase over time. While it is possible to decrease the entropy of a small part of a system, the overall entropy of the entire system will still increase.

5. How is the concept of entropy related to the arrow of time?

The arrow of time refers to the idea that time only moves in one direction, from the past to the future. This is closely related to the concept of entropy, as the second law of thermodynamics dictates that the entropy of a closed system will always increase over time. This means that the past has less entropy than the future, which is why we perceive time as moving forward.

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