Entropy vs Temp graphfind Volume?

In summary, the conversation is about finding the volume V_2 using a Temp vs. Entropy graph and the first law of thermodynamics. The first law is applied to the cyclical path, with the area under the curve representing the total Q of the system. The work done in the cycle is equal to the total Q, and this can be used to relate to V_2. The conversation also mentions using the fact that dS=\frac{\delta Q}{T} and that at point 1, V_1=.2m^2. The relationship between \Delta Q and W is also discussed, and it is mentioned that knowing everything except V_f can help solve for V_f.
  • #1
Roger Wilco
30
0
Entropy vs Temp graph..find Volume??

Homework Statement



Photo1.jpg



I need to find V_2 by usinf the Temp vs. Entropy graph attached.

It says as a hint to use part b in which I found [tex]Q_{23}=0[/tex] by finding the area

under the curve (where ds=0).


Homework Equations

Since Q=0 I know [tex]\Delta E_{int}=-W=nC_v\Delta T[/tex] but I am completely stumped! I know delta T, I know n, R...but I don't know any Vs or pressures.

Where do I start?!


I need some hints!
Thanks,
RW
 
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  • #2
I'm dyin' over here! Any ideas..i've been looking at this one since yesterday?!
 
  • #3
Damn...
 
  • #4
Roger Wilco said:

I need to find V_2 by usinf the Temp vs. Entropy graph attached.

It says as a hint to use part b in which I found [tex]Q_{23}=0[/tex] by finding the area

under the curve (where ds=0).

Homework Equations

Since Q=0 I know [tex]\Delta E_{int}=-W=nC_v\Delta T[/tex] but I am completely stumped! I know delta T, I know n, R...but I don't know any Vs or pressures.

Where do I start?!I need some hints!
Try the first law:

[tex]dQ = TdS = dU + PdV[/tex]

What is the area inside the path? (ie the sum of the areas under each path)? What does that represent?

What is the work done in that cycle? How is that work related to V2?AM
 
Last edited:
  • #5
Andrew Mason said:
Try the first law:

[tex]dQ = TdS = dU + PdV[/tex]

What is the area inside the path? (ie the sum of the areas under each path)? What does that represent?

What is the work done in that cycle? How is that work related to V2?


AM

The area inside the triangle abc= the total Q of the system right? I know that is cyclical so Delta E total is 0...So total W=total Q, but I am still having trouble relating this to Volume of 2?

RW
 
  • #6
So it seems that my instructor left out the fact that at point 1, V_1=.2m^2.
And I am supposed to used the fact that [itex]dS=\frac{\delta Q}{T}[/itex] to find V_2. I know that 1-->2 is an isotherm, but I do not see how that would help. I that along the isotherm, [itex]W=nRT\ln\frac{V_f}{V_i}[/itex] but I don't see hpw that helps either? It isn't like I can solve for V_f if I know V_i and W is it?

RW
 
  • #7
Roger Wilco said:
So it seems that my instructor left out the fact that at point 1, V_1=.2m^2.
And I am supposed to used the fact that [itex]dS=\frac{\delta Q}{T}[/itex] to find V_2. I know that 1-->2 is an isotherm, but I do not see how that would help.
Yes. What is [itex]\Delta U[/itex] if there is no temperature change? What, then, is the relationship between [itex]\Delta Q \text{ and } W[/itex]?.

I that along the isotherm, [itex]W=nRT\ln\frac{V_f}{V_i}[/itex] but I don't see hpw that helps either? It isn't like I can solve for V_f if I know V_i and W is it?
Why not?
You know everything except Vf once you work out the relationship between W and Q.

AM
 

1) How does entropy change with temperature in a volume?

The relationship between entropy and temperature in a volume depends on the material and its physical properties. In general, as the temperature increases, the entropy of a material also increases. This is due to the increased molecular motion and disorder at higher temperatures. However, there are exceptions to this trend, such as when a material undergoes a phase change.

2) What is the significance of the slope of an entropy vs. temperature graph?

The slope of an entropy vs. temperature graph represents the change in entropy per unit change in temperature. A steeper slope indicates a higher rate of change in entropy with temperature, while a flatter slope indicates a lower rate of change. The slope can also provide information about the physical properties of the material, such as the heat capacity and phase transitions.

3) How does the entropy of a gas change with temperature?

For an ideal gas, the entropy increases as the temperature increases. This is because the molecules in a gas have more freedom to move and disperse at higher temperatures, leading to increased disorder and therefore higher entropy. However, for real gases, the relationship between entropy and temperature may be more complex, as it depends on factors such as intermolecular interactions.

4) Can the entropy of a system decrease with increasing temperature?

In most cases, the entropy of a system will increase with increasing temperature. However, there are some exceptions, such as when a material undergoes a phase transition. In this case, the entropy may decrease during the transition from a more ordered phase to a less ordered phase, even though the temperature is increasing. Additionally, in some cases, the entropy may reach a maximum and then decrease with further temperature increases.

5) What is the relationship between entropy and temperature in a reversible process?

In a reversible process, the entropy of a system remains constant. This means that as the temperature increases, the entropy also increases, but at a rate that balances the decrease in entropy due to the decrease in temperature. This relationship is described by the equation ΔS = Q/T, where ΔS is the change in entropy, Q is the heat added or removed from the system, and T is the temperature. In this case, the slope of the entropy vs. temperature graph is zero, indicating a constant entropy.

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