- #1
Jennifer Lyn
- 5
- 0
Like in the other problem I posted- This is the other question that I missed and just can't find a solution for.
Prove the internal pressure is 0 for an ideal gas and ((n^2)a)/(v^2) for a Van der Waals gas.
1. VdQ Eqn: p= (nRT)/(v-b) - ((n^2)a)/(v^2)
2. (partial S/partial V) for constant T = (partial p/partial T) for contant V.
3. dU = TdS - pdV
4. pi sub t (internal pressure) = (partial U/partial V) for constant T
a) Ideal Gas
0 = (partial U/partial V) for const T
int 0 dv = int du
0 = int (TdS - pdV)
int p dv = int T ds
int (nRT/v) dv = int (Pv/nR) dS
nRT x int(1/V) dv = pv/nR x int 1 dS
... and I get kind of lost here, though I know that what I've already done is wrong.. :(
b) VdW gas
I actual have to get going to school, but I'll come back and type up what I've done (incorrectly :( for this part afterwards).
Homework Statement
Prove the internal pressure is 0 for an ideal gas and ((n^2)a)/(v^2) for a Van der Waals gas.
Homework Equations
1. VdQ Eqn: p= (nRT)/(v-b) - ((n^2)a)/(v^2)
2. (partial S/partial V) for constant T = (partial p/partial T) for contant V.
3. dU = TdS - pdV
4. pi sub t (internal pressure) = (partial U/partial V) for constant T
The Attempt at a Solution
a) Ideal Gas
0 = (partial U/partial V) for const T
int 0 dv = int du
0 = int (TdS - pdV)
int p dv = int T ds
int (nRT/v) dv = int (Pv/nR) dS
nRT x int(1/V) dv = pv/nR x int 1 dS
... and I get kind of lost here, though I know that what I've already done is wrong.. :(
b) VdW gas
I actual have to get going to school, but I'll come back and type up what I've done (incorrectly :( for this part afterwards).