# Isothermal Process

1. Sep 7, 2009

### aznmaverick

1. The problem statement, all variables and given/known data
Calculate Q(in) and Q(out).

2. Relevant equations
Specific Heat: Cv = 5/2 R
R = 8.314 J/mol K

3. The attempt at a solution
For the process C-> A, it is an isothermic process but we are not given temperature. The equation to finding the total work done from C->A is nRT ln (Va/Vc). How do I get T in order to solve for nRT ln (Va/Vc)?

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2. Sep 8, 2009

### Mapes

Hint: is there a constitutive equation for this substance?

3. Sep 8, 2009

### aznmaverick

Yes, I got that from Q (from C to A) = Delta U (C to A) + W (C to A) and since Delta U (C to A) = 0, Q (C to A) = W ( C to A).
W (C to A) for an isothermal process is = (Integral from C to A) P dv

Using the formula PV = nRT and solving for P, we get P = nrT/V, so W (C to A) = (Integral from C to A) nRT/V dv, which comes out to be nRT ln v (from C to A). Finally plugging in C and A, we get nRT ln (Va - Vc) = nRT ln (Va/Vc)

4. Sep 8, 2009

### Mapes

The value of $nRT$ can be easily calculated even though neither n nor T are known. Know what I mean?

5. Sep 8, 2009

### aznmaverick

Yes, well, n=1 mole, and T is unknown, but we know that its a constant. So we cannot solve for it?

6. Sep 8, 2009

### Mapes

How do you know that there's one mole present? Is there more information in the problem statement that you didn't post?

In any case, the ideal gas law connects all these variables together.

7. Sep 8, 2009

### aznmaverick

Yea, 1 mole was a given. T is still not given. So does that mean theres no 'real answer' to this question w/o T given?

8. Sep 8, 2009

### Mapes

If P, V, and n are known for an ideal gas, then T is known.

9. Sep 8, 2009

### aznmaverick

Got it, thanks!