# Entropy vs Temp graphfind Volume?

1. Dec 9, 2007

### Roger Wilco

Entropy vs Temp graph..find Volume?!?!

1. The problem statement, all variables and given/known data

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).

2. Relevant 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

2. Dec 9, 2007

### Roger Wilco

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

3. Dec 9, 2007

Damn....

4. Dec 9, 2007

### Andrew Mason

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

Last edited: Dec 9, 2007
5. Dec 10, 2007

### Roger Wilco

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. Dec 10, 2007

### 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

7. Dec 12, 2007

### Andrew Mason

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

Why not?
You know everything except Vf once you work out the relationship between W and Q.

AM