What is the result of application of this equation to an ideal gas ?
b.) Heat capacities CP and CV are defined as temperature derivatives respectively of U and H. Because these properties are realted, one expects the heat capacities also to be related. Show that the general expression connecting CP to CV is:
Show that equation B of example 6.2 is another form of this expression.
6 comments:
Hey, you don't have to do the last part of this problem:
"Show that equation B of example 6.2 is another form of this expression."
It isn't hard just look at Eqns 3.2 and 6.34.
I just cancelled this part because we did not discuss beta and kappa in class. You can read a bit about them on page 68 if you are curious.
I'm having a little trouble with getting this problem started. I first thought I could start by moving the dt and dp around to get things that cancel out or convert to Cp. That led me to a dead end.
Then I started again by using the relations of equations of 6.13-6.19. Again nowhere.
Does anyone have any tips on how to start this problem? Maybe if someone could explain how to use the fact that this is an exact differential I would be less confused.
confused 5:15 pm
Start from the definition of exactness. The order of differentiation does not matter. In this case, Cp = {dH/dT}P, so {dCp/dP}T = {d2H/dT dP}. Next look at the 2nd term in Eqn 6.20.
I have it that the equation equals d^2H/dPdT and from there i can substitute eq. 6.20 for dh this gives me: (dv/dt)-(t*d^2v/dt^2). The second term in my final equation is what I want so is there a reason why dv/dt would equal zero in this case? Or do you see something i did wrong?
Erik 6:52 PM:
{dV/dT}P is not zero, but {d2V/dT2}P = 0. I cannot tell you much more based on the information you have provided.
Here are a few hits I have shared with others offline...
Setup an HPP that first takes reactants to products at 25C and 1 bar. Then, split-up the C2H2 and the solid so you can calc delta-H and delta-S for each of them. The C2H2 at 1 bar and 25C can be considered an IG. Change the T & P to the final T and P and calc delta-H and delta-S for each step. Finaly, calc the Hr and Sr for taking the IG back to the real state at the final T and P. You also need to calc delta-H and delta-S for the solid.
It is important to add up delta-H and delta-S and NOT the molar or wiggle versions of these variables. You cannot add delta-S-wiggle for C2H2 to one for the solid because they are per mole of different quantities.
You determine the final P FIRST because you know both T and Vwiggle of the gas. Be sure to subtract the volume of the solid from the total volume of the vessel. Just plug in the values.
You must use SRK directly to get P2 AND you must use it to get the residual H and S.
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