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### Topic: i am confused... cp and cv  (Read 42608 times)

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#### fkatzenb

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##### i am confused... cp and cv
« on: September 16, 2005, 02:15:11 PM »
i have confused my self in terms of cp and cv and what they actually mean. anyone help?

with a isentropic compression, i am using volume as my known component and getting rid of the gas constant to wind up with the following equation....

p2 / p1 = (v1 / v2) ^ (gamma)
T2/T1 = ([v1 / v2]^[gamma])^[(gamma - 1)/gamma)]
gamma = specific heat ratio = cp/cv

what i dont understand is how to properly look up cp and cv.  since i am looking for pressure and temperature at many different points thru the compression.  so my assumption is that for each point, i have to find a cp and cv for both the pressure and temperature of p1.  is this true?

thanks!
Frank

#### Donaldson Tan

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##### Re:i am confused... cp and cv
« Reply #1 on: September 19, 2005, 03:10:30 AM »
cp is heat capacity at constant pressure

cv is heat capacity at constant volume

the beauty of perfect gas is that it have a constant cp:cv ratio.

i am not too sure how that applies to a real gas. hope others can help.
« Last Edit: September 19, 2005, 03:13:48 AM by geodome »
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#### Juan R.

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##### Re:i am confused... cp and cv
« Reply #2 on: September 19, 2005, 05:22:19 AM »
Hi, geodome

For "real" -i dislike term 'real' because all scientific models are always ideal- gas

Cp - Cv = [T Vm (alpha)^2] / kappaT

where

Vm is molar volume, alpha is the coefficient of expansion, and kappaT the isothermal compressibility.

For an "ideal" -i dislike term 'ideal' gas because all models of gases are obviously ideal-gas,

Cp - Cv = R
« Last Edit: September 19, 2005, 05:23:21 AM by Juan R. »
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#### fkatzenb

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##### Re:i am confused... cp and cv
« Reply #3 on: September 19, 2005, 08:40:11 AM »
What I mean is how they apply to isentropic compression.  Constant pressure and constant volume is far from what is actually happening in the system.

#### Donaldson Tan

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##### Re:i am confused... cp and cv
« Reply #4 on: September 19, 2005, 04:02:53 PM »
but the process can be approximated by regarding it as a series of isobaric and isochoric changes.
"Say you're in a [chemical] plant and there's a snake on the floor. What are you going to do? Call a consultant? Get a meeting together to talk about which color is the snake? Employees should do one thing: walk over there and you step on the friggin� snake." - Jean-Pierre Garnier, CEO of Glaxosmithkline, June 2006

#### fkatzenb

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##### Re:i am confused... cp and cv
« Reply #5 on: September 19, 2005, 10:53:00 PM »
but the process can be approximated by regarding it as a series of isobaric and isochoric changes.

I have problems formulating my thoughts.  I had a discussion today who is a chemist.  He told me to varify it on here with you all.

Here was my problem.  It was the interpetation of cp and cv that I was having difficulty with.  When going from v1 to v2, you have to setup  what p1 and t1 was to determine cp and cv.  My problem was looking for values and how to look for the value.  It was my impression that I had to look up a both a cp and cv value for that pressure and that temperature.  however, for example, cp values are typically in a table for 1atm with variable temperature.  so i was at a lost.  however he is saying that the nature/definition of cp is that its at 1atm and that its all good.  I just need to reference the temp and I have cp.  Now he says it maybe easier to find the gas constant to find cv... tables are rare?

Frank

#### Juan R.

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##### Re:i am confused... cp and cv
« Reply #6 on: September 24, 2005, 05:39:40 AM »
You are not saying many about your problem, here general solution. I hate to use 'real' and 'ideal' because any model is always ideal, but i will use standard notation

CV, real = CV, ideal + A

A = IinfiniteV T (d2Tp) dV

"I" is integral and (d2T) denotes second derivative of p respect to T.

Once known CV. real can compute CP. real. Do you need or either equation of state of your model (there are thousand of equations available in engineering literature, Geodome can explain this better than me) or an empirical fit with you system.
« Last Edit: September 24, 2005, 05:42:07 AM by Juan R. »
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