Ideal Gas Equation vs Isentropic Equation

[Joethebro]

I have a question concerning usage of the combined gas law (PV/T = constant) vs an isentropic equation (e.g., (P2/P1) = (T2/T1)^(k/(k-1))). How do you know when to use which formula?

For example, if I had a gas where volume was held constant, but temperature was increased, which of the following equations would I use and why:

(P2/T2) = (P2/T2)

(P2/P1) = (T2/T1)^(k/(k-1))

 

[zdas04]

Does the process involve work done on or by the fluid? If so, is the process adiabatic (i.e., is it isentropic and reversible)? If so use the adiabatic equation (what you called the isentropic equation). If it is not reversible, then you need to find another equation of state.

On the other hand if your gas is not air, then you should be using the real gas equation (PV/(nTZ)=Constant (R)) instead of the ideal gas equation.

The difference between the two equations you gave is work done on or by the fluid. To calculate outlet temperature of a compressor, you use the adiabatic equation. To calculate a new pressure when a volume of a fixed mass of gas is heated, use the real (or ideal) gas equation.

David Simpson, PE
MuleShoe Engineering

"Belief" is the acceptance of an hypotheses in the absence of data.
"Prejudice" is having an opinion not supported by the preponderance of the data.
"Knowledge" is only found through the accumulation and analysis of data.
The plural of anecdote is not "data"

 

[zekeman]

You meant


(1) (P2/T2) = (P1/T1)
P2/P1=T1/T2 constant volume
(2) (P2/P1) = (T2/T1)^(k/(k-1)) must have volume change
The first equation is universal and is valid for any ideal gas under any conditions
The second is a reversible process in which work is done on or by the medium which implies that the volume MUST change,since you can't do work on or by the medium without a volume change,violating your constant volume scenario.

 

[Latexman]

Oops!

(1) (P1/T1) = (P2/T2)
P1/P2=T1/T2 constant volume


Good luck,
Latexman

Need help writing a question or understanding a reply? forum1529

 

[zdas04]

The first equation is universal and is valid for any ideal gas under any conditions

What planet are you doing Engineering on? I cannot think of a single equation that applies to a fluid that that statement would be true. In fact the equation you are calling "the first equation" is OK for ideal gas (the only ones I know of are Air and Nitrogen). It is nearly never true for changes in excess of about 15% or either temperature or pressure of non-ideal gases. It is only true-ish of air if you can ignore the 2% deviation from ideal behavior around 80 bara. It is not true for air if you introduce more air or allow some to leak out since the equation is really PV=nRT for ideal gases not P/T=constant. If you've allowed mass to enter or leak out then you can't cancel the "n" term.

David Simpson, PE
MuleShoe Engineering

"Belief" is the acceptance of an hypotheses in the absence of data.
"Prejudice" is having an opinion not supported by the preponderance of the data.
"Knowledge" is only found through the accumulation and analysis of data.
The plural of anecdote is not "data"

 

[zdas04]

Oh yeah, a gas turning a turbine is a constant volume process that does not follow the ideal or real gas laws.

David

 

[zekeman]

" The first equation is universal and is valid for any ideal gas under any conditions"

If you bothered to look, I said "IDEAL GAS"

 

[zdas04]

With enough qualifiers, it might be true for an ideal gas. You would have to have a situation with:
[ul]
[li]Constant volume[/li]
[li]Zero leakage of gas from the volume[/li]
[li]Zero added gas to the volume[/li]
[li]Zero chemical reactions within the volume (e.g., you would have to keep sunlight out since high energy photons cause chemical changes in many gases)[/li]
[li]A gas that did actually behave in an ideal manner. Nitrogen and Air are generally close enough for Engineering work, but no gas is actually ideal[/li]
[/ul]

That is a lot of assumptions for something that is "valid for any ideal gas under any conditions".

David Simpson, PE
MuleShoe Engineering

"Belief" is the acceptance of an hypotheses in the absence of data.
"Prejudice" is having an opinion not supported by the preponderance of the data.
"Knowledge" is only found through the accumulation and analysis of data.
The plural of anecdote is not "data"

 

[zekeman]

"What planet are you doing Engineering on? I cannot think of a single equation that applies to a fluid that that statement would be true. In fact the equation you are calling "the first equation" is OK for ideal gas (the only ones I know of are Air and Nitrogen). It is nearly never true for changes in excess of about 15% or either temperature or pressure of non-ideal gases. It is only true-ish of air if you can ignore the 2% deviation from ideal behavior around 80 bara. It is not true for air if you introduce more air or allow some to leak out since the equation is really PV=nRT for ideal gases not P/T=constant. If you've allowed mass to enter or leak out then you can't cancel the "n" term. "


BTW, what does this blather have anything yo do with the OP
question?

 

[Latexman]

joethebro,

Going strictly by "volume was held constant, but temperature was increased", (P1/T1) = (P2/T2) applies. Because volume was held constant (no work was done to change the volume).

http://en.wikipedia.org/wiki/Gas_laws

http://en.wikipedia.org/wiki/Gas_compression

Good luck,
Latexman

Need help writing a question or understanding a reply? forum1529

 

[zekeman]

"With enough qualifiers, it might be true for an ideal gas. You would have to have a situation with:

Constant volume
Zero leakage of gas from the volume
Zero added gas to the volume
Zero chemical reactions within the volume (e.g., you would have to keep sunlight out since high energy photons cause chemical changes in many gases)
A gas that did actually behave in an ideal manner. Nitrogen and Air are generally close enough for Engineering work, but no gas is actually ideal

That is a lot of assumptions for something that is "valid for any ideal gas under any conditions".



This is preposterous.
Are you a lawyer or an engineer?
I never saw anybody take a simple question and give such a convoluted response.
I'm done with this nonsense.

 

[sailoday28]

PV/T=constant is good for all gases as pressure approaches 0
The P2/P1 equations is good for the ideal gas with constant specific heats undergoing a reversible adiabatic (heat trans=0) process.

Regards