Entropy vs Temp graphfind Volume?

[Roger Wilco]

Entropy vs Temp graph..find Volume??

Homework Statement

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 $$Q_{23}=0$$ by finding the area

under the curve (where ds=0).

Homework Equations

Since Q=0 I know $$\Delta E_{int}=-W=nC_v\Delta T$$ 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

 

[Roger Wilco]

I'm dyin' over here! Any ideas..i've been looking at this one since yesterday?!

 

[Roger Wilco]

Damn...

 

[Andrew Mason]

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 $$Q_{23}=0$$ by finding the area

under the curve (where ds=0).

Homework Equations

Since Q=0 I know $$\Delta E_{int}=-W=nC_v\Delta T$$ 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:

$$dQ = TdS = dU + PdV$$

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

 

[Roger Wilco]

Try the first law:

$$dQ = TdS = dU + PdV$$

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

 

[Roger Wilco]

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 $dS=\frac{\delta Q}{T}$ 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, $W=nRT\ln\frac{V_f}{V_i}$ 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

 

[Andrew Mason]

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 $dS=\frac{\delta Q}{T}$ to find V_2. I know that 1-->2 is an isotherm, but I do not see how that would help.

Yes. What is $\Delta U$ if there is no temperature change? What, then, is the relationship between $\Delta Q \text{ and } W$?.

I that along the isotherm, $W=nRT\ln\frac{V_f}{V_i}$ 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