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Thyferra2680
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For a gas that obeys the equation of State P(v-b) = RT, where b is a constant, show that Cp is independent of Pressure, i.e., ([tex]\delta[/tex]Cp/[tex]\delta[/tex]p) at constant T is equal to zero
Maxwell Relations
H = U+PV
dh = TdS + PdV
dh/dT at constant P is defined as Cp
Unfortunately I can't simply say that since Cp is defined as existing at a constant pressure state, that it's independent of pressure; would have made the problem much simpler.
I figure that I'm supposed to prove that ([tex]\delta[/tex](dH/dT)/[tex]\delta[/tex]p) at constant T is equal to zero, but I'm having trouble figuring out which maxwell relation is the best fit.
d/dP (dH/dT) = d[((TdS)/dT + (VdP)/dT) at constant P]/dP at constant T
My problem is the dS portion of the equation. It's defined in terms of Cp, among other things, and that doesn't really help me in any way... I think.
I have a similar problem when I attempt it with dH = d(U+PV). dU is defined in terms of Cv, or if I break it apart with U = Q+W, I get U = TdS- PdV. Again, not too helpful.
Is it an issue of which relation I'm using to start? Or can the Cv and Cp actually help me?
Thanks for the help
Homework Equations
Maxwell Relations
H = U+PV
dh = TdS + PdV
dh/dT at constant P is defined as Cp
The Attempt at a Solution
Unfortunately I can't simply say that since Cp is defined as existing at a constant pressure state, that it's independent of pressure; would have made the problem much simpler.
I figure that I'm supposed to prove that ([tex]\delta[/tex](dH/dT)/[tex]\delta[/tex]p) at constant T is equal to zero, but I'm having trouble figuring out which maxwell relation is the best fit.
d/dP (dH/dT) = d[((TdS)/dT + (VdP)/dT) at constant P]/dP at constant T
My problem is the dS portion of the equation. It's defined in terms of Cp, among other things, and that doesn't really help me in any way... I think.
I have a similar problem when I attempt it with dH = d(U+PV). dU is defined in terms of Cv, or if I break it apart with U = Q+W, I get U = TdS- PdV. Again, not too helpful.
Is it an issue of which relation I'm using to start? Or can the Cv and Cp actually help me?
Thanks for the help