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JeffEvarts
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- TL;DR Summary
- I have a compressed pure gas at a specific temperature and volume. It suddenly (adiabatically) expands until it's at ambient pressure and a specific temperature, T2. Given: T1, V1, T2, and P2, I want to find P1 and V2.
I have a compressed pure gas at a specific temperature and volume. (T1, V1) It suddenly (adiabatically) expands until it's at ambient pressure and a specific temperature. (P2, T2). Given: T1, V1, T2, and P2, I want to find P1 and V2.
There's a great example in wikipedia which is almost exactly this case, with compression rather than expansion, and I can't seem to generalize the math. Grr.
Here it is: Example of adiabatic compression
It starts with room temp air and compresses it into 1/10 the volume.
So far, so good. High school physics: k = P1V1/T1 = P2V2/T2. From that, I can figure out what the ratio of the temperature and pressure will be: V goes down by a factor of 10, T/P varies by the same factor.
The math on the page goes farther than that, though, and gives individual values for P and T. That's where I get lost. It feels like (as a college grad in a technical major) I should be able to do this algebra, but I keep getting nonsense at the end.
Can anyone offer me a pair of formulas to solve for P1 and V2 in whatever "common" case you like?
So just so we're all on the same page, here are some approximate values I'm working with:
P1 = ? // something quite large. 10atm? more?
T1 = 263K // -10C
V1 =1L
P2 = 101kPa // 1 atm
T2 = 193K // -80C
V2 = ? //something quite large. 10L? more?
NB: The gas is "pure" CO2 so the "7/5" exponent may be inappropriate.
Thank you for your attention,
-Jeff Evarts
There's a great example in wikipedia which is almost exactly this case, with compression rather than expansion, and I can't seem to generalize the math. Grr.
Here it is: Example of adiabatic compression
It starts with room temp air and compresses it into 1/10 the volume.
So far, so good. High school physics: k = P1V1/T1 = P2V2/T2. From that, I can figure out what the ratio of the temperature and pressure will be: V goes down by a factor of 10, T/P varies by the same factor.
The math on the page goes farther than that, though, and gives individual values for P and T. That's where I get lost. It feels like (as a college grad in a technical major) I should be able to do this algebra, but I keep getting nonsense at the end.
Can anyone offer me a pair of formulas to solve for P1 and V2 in whatever "common" case you like?
So just so we're all on the same page, here are some approximate values I'm working with:
P1 = ? // something quite large. 10atm? more?
T1 = 263K // -10C
V1 =1L
P2 = 101kPa // 1 atm
T2 = 193K // -80C
V2 = ? //something quite large. 10L? more?
NB: The gas is "pure" CO2 so the "7/5" exponent may be inappropriate.
Thank you for your attention,
-Jeff Evarts
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