Understanding Entropy: Drawing Temperature Entropy Graphs

In summary, the conversation discusses the equation for entropy in ideal gas transformations and the difficulty in applying it to drawing a temperature entropy graph. It is noted that in an adiabatic compression, the entropy should theoretically change, but the equation does not reflect this. The question is raised about guidelines for drawing the graph and determining the curve's concavity or convexity. It is suggested that a change in temperature may have little effect on entropy if Cv is small and Rl is large. The conversation also mentions an isobaric heating scenario and asks for help in determining the curvature of its temperature entropy curve.
  • #1
Delzac
389
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Homework Statement


Hi all,

Is there anyway, meaning by use of equation to determine how we should draw a temperature entropy graph?

I understand that is the equation for entropy for ideal gas transformation:

[tex] \del S = nC_vln(\frac{T_f}{T_i}) + nRln(\frac{V_f}{V_i}) [/tex]

But i don't seem to be able to apply it very well.

For example, in a adiabatic compression, the entropy doesn't change but temperature does (appears as straight line on graph). Yet, the equation tells me that there should be change in entropy. That is, if i understanding is not wrong.

So it there any generally guidelines to drawing the graph, and whether the curve is concave or convex.
 
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  • #2
I’m not familiar with this, but if Cv was small and Rl was large then entropy wouldn't change (much) if T did. You are taking the natural log of T so a change would have little effect, and if the right side of the + was a large number then a small change on the left side of the + would not make much difference to entropy.
 
  • #3
How about, say a isobaric heating, how would one then determine the curvature of its temperature entropy curve?

Any help from anyone will be greatly appreciated.
 
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FAQ: Understanding Entropy: Drawing Temperature Entropy Graphs

What is entropy and why is it important?

Entropy is a measure of the disorder or randomness in a system. In scientific terms, it is the tendency of a system to move from a state of order to a state of disorder. It is an important concept in thermodynamics, as it helps us understand the spontaneity of chemical reactions and the direction of heat flow.

How is entropy represented on a graph?

Entropy is typically represented on a graph with entropy on the y-axis and temperature on the x-axis. The graph is usually a curve that increases as the temperature increases. The slope of the curve represents the change in entropy with respect to temperature.

What factors affect the shape of an entropy graph?

The shape of an entropy graph is affected by several factors, including the complexity of the system, the number of particles in the system, and the temperature. As the complexity and number of particles increase, the curve becomes steeper. At higher temperatures, the curve becomes more gradual.

How can we interpret an entropy graph?

An entropy graph can provide valuable information about a system. The slope of the curve can tell us about the changes in entropy with respect to temperature, and the area under the curve can give us the total change in entropy. Additionally, the shape of the curve can indicate the complexity of the system and how it changes with temperature.

Can an entropy graph be used to predict the behavior of a system?

Yes, an entropy graph can be used to predict the behavior of a system. By analyzing the shape of the curve and the changes in entropy, we can make predictions about the spontaneity of reactions and the direction of heat flow. However, it is important to note that an entropy graph is just one tool in understanding a system and should be used in conjunction with other scientific principles.

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