Isothermal Process Homework: Calculate Q(in) & Q(out)

[aznmaverick]

Homework Statement

Calculate Q(in) and Q(out).

Homework Equations

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

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)?

 

[Mapes]

How do I get T in order to solve for nRT ln (Va/Vc)?

Hint: is there a constitutive equation for this substance?

 

[aznmaverick]

Hint: is there a constitutive equation for this substance?

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)

 

[Mapes]

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

 

[aznmaverick]

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

 

[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.

 

[aznmaverick]

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.

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

 

[Mapes]

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

 

[aznmaverick]

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

Got it, thanks!