Posted by J. Clarke on January 2, 2011, 2:36 pm
>
> On 1/1/2011 1:43 PM, daestrom wrote:
> > On 12/31/2010 12:47 PM, Morris Dovey wrote:
>
> >> The challenge appears to be allowing (and controlling) the expansion in
> >> such a way that the water remains fluid, and leveraging the high
> >> pressure / low expansion efficiently in the neighborhood of the critical
> >> temperature.
> >>
> >> It seems like it should be possible - and there may be some interesting
> >> solar possibilities if it can be done...
> >
> > If you let it expand enough to change phase, then you can *really* boost
> > the power output. Expanding steam and 'compressing' only liquid water
> > yields a lot of net work. :-)
>
> Ok. I think that's easily managed. I suppose I shouldn't be surprised
> that this part of the pump project now appears headed almost directly
> toward a scaled-up and slightly-modified version of Sno's "pop-pop" engine.
>
> > Problem is, it's been done to death. That's a steam engine pure and
> > simple (expand steam in a cylinder/turbine, 'compress' water in a
> > feed-pump).
>
> Then so be it. The way it's shaping up, the "compression" mechanism will
> probably be a a pump output column/standpipe arrangement.
>
> I don't particularly mind that it's been done to death. If I could find
> a combined engine/pump design that could be driven with solar heat and
> that could be built in a third world bicycle shop for under US$00, I
> could skip this entire exercise and remain blissfully ignorant.
>
> I've probably become over-sensitized, but every news report telling
> about crisis conditions in just about any underdeveloped area seems to
> point to non-availability of water as at least a primary factor - and
> it's not that there isn't any, it's simply in the wrong place - and the
> folks with the problems lack the means to get it.
>
> "Steam Tables (English Units)" by Keyes et al arrived yesterday
> afternoon, and I've been immersed in the appendix a good part of the
> time since. I'm in the process of turning "The Fundamental Equation"
> (Helmholtz free energy) into a trio of C subfunctions - and, as usual, I
> can say that I now know even /more/ that I don't understand. :)
>
> Kinda hoping that Wark's "Thermodynamics" shows up soon to help me
> better understand what I'm attempting...
I should have mentioned it before, but if you're a new to thermo or it's
been a long time since you took the course, you might want to work
through the Schaums <
(Amazon.com product link shortened)
Thermodynamics-Engineers-2ed/dp/0071611673/ref=pd_cp_b_1#_> as well.
Posted by daestrom on December 24, 2010, 7:15 pm
On 12/24/2010 12:38 PM, Morris Dovey wrote:
> Given the Ideal Gas Law: PV = nRT
> If some volume of an ideal gas is captured in a closed container at STP
> (293.15K, 1 atm), it appears that V, n, and R should be constant.
Actually, for chemistry and ideal gas purposes, STP is defined as 1 atm
and 273.15K (0 C), not 293.15K (20 C).
> Rearranging gives P = nRT/V = (n/V)RT
> I recall that at STP, 1 mole of a gas occupies a 22.4 L volume - which
> should allow me to write n/V = 1/22.4 and use R = 0.08205746 Latm/Kmol
> to get
> P = (0.08205746/22.4)*T = 0.00366328*T atm
> To arrive at a (P,T) relationship that is independent of the actual
> number of moles of the gas and/or the actual volume of the container.
> This plots as a straight line passing through (P=0,T=0) with a slope of
> (approximately) 0.00366328 atm/K (or atm/°C)
> This seems too easy - and strikes me as too small. Have I made a wrong
> assumption or miscalculated somewhere here?
This is valid for 'ideal' gasses and only if the volume is held constant.
But in a lot of thermodynamics you have to consider a change in the
(n/V) term. Then it gets a bit more complicated (but not too bad).
For a fixed mass of gas, we can get a couple of different formulas
depending on what process you're interested in.
For constant volume:
T1/T2 = P1/P2 (this is what you have above)
For constant temperature:
V1/V2 = P2/P1 (PV= K )
Both of the above however require that you add/remove heat as either T
or V changes.
For the case of expansion or compression where there is little time for
heat to be transferred in/out, (i.e. the process is adiabatic), we have:
PV^y = K
Where y is the ratio of specific heats (1.4 for air, 1.66 for monoatomic
gases and 1.3 for steam). You can combine this with the ideal gas law
(PV=nRT) and find the temperature change during compression/expansion as
well as volume changes. Substitute P=nRT/V into the above and you get:
nRTV^(y-1) = K
yielding
T1/T2 = (V2/V1)^(y-1)
Or substituting V=nRT/P, we get
T1/T2 = (P2/P1)^(1-y)/y
Good Luck
daestrom
Posted by Morris Dovey on December 24, 2010, 8:21 pm
On 12/24/2010 1:15 PM, daestrom wrote:
> On 12/24/2010 12:38 PM, Morris Dovey wrote:
>> If some volume of an ideal gas is captured in a closed container at STP
>> (293.15K, 1 atm), it appears that V, n, and R should be constant.
>
> Actually, for chemistry and ideal gas purposes, STP is defined as 1 atm
> and 273.15K (0 C), not 293.15K (20 C).
Ok. I found multiple definitions and used the one with which the 22.4
liter/mole figure was associated. Do I need to adjust that if I use 0°C
as the Standard Temperature?
>> This plots as a straight line passing through (P=0,T=0) with a slope of
>> (approximately) 0.00366328 atm/K (or atm/°C)
> This is valid for 'ideal' gasses and only if the volume is held constant.
<grin> Understood, but I'm such a rank beginner that these are exactly
the conditions I'm struggling to establish as a baseline...
> But in a lot of thermodynamics you have to consider a change in the
> (n/V) term. Then it gets a bit more complicated (but not too bad).
I kinda wondered about that, and I decided that I'd better wrap my head
around the most simple case first - then add complications as necessary.
> For a fixed mass of gas, we can get a couple of different formulas
> depending on what process you're interested in.
>
> For constant volume:
> T1/T2 = P1/P2 (this is what you have above)
>
> For constant temperature:
> V1/V2 = P2/P1 (PV= K )
>
> Both of the above however require that you add/remove heat as either T
> or V changes.
So far so good. In what actually I'm working on, neither the volume nor
the temperature will be constant - but examining the beast with a
constant volume assumed seems like a good starting point.
> For the case of expansion or compression where there is little time for
> heat to be transferred in/out, (i.e. the process is adiabatic), we have:
>
> PV^y = K
Ah - you've just touched on one of the really big holes in my mental
model: time. I'm a long way (I think) from incorporating a t variable
into the process. Methinks I'm going to spend a fair amount of time
learning heat transfer basics to satisfy that need.
> Where y is the ratio of specific heats (1.4 for air, 1.66 for monoatomic
> gases and 1.3 for steam). You can combine this with the ideal gas law
> (PV=nRT) and find the temperature change during compression/expansion as
> well as volume changes. Substitute P=nRT/V into the above and you get:
>
> nRTV^(y-1) = K
> yielding
> T1/T2 = (V2/V1)^(y-1)
>
> Or substituting V=nRT/P, we get
> T1/T2 = (P2/P1)^(1-y)/y
Hmm - forewarned is forearmed. This looks like Good Stuff so I've filed
a copy of your response for future reference. For the moment I'm going
to stick with dry air or pure water for modeling, although I'm beginning
to suspect that air will be of decreasing interest.
Many, many thanks!
--
Morris Dovey
http://www.iedu.com/DeSoto/
PGP Key ID EBB1E70E
Posted by J. Clarke on December 25, 2010, 1:09 am
>
> On 12/24/2010 1:15 PM, daestrom wrote:
> > On 12/24/2010 12:38 PM, Morris Dovey wrote:
>
> >> If some volume of an ideal gas is captured in a closed container at STP
> >> (293.15K, 1 atm), it appears that V, n, and R should be constant.
> >
> > Actually, for chemistry and ideal gas purposes, STP is defined as 1 atm
> > and 273.15K (0 C), not 293.15K (20 C).
>
> Ok. I found multiple definitions and used the one with which the 22.4
> liter/mole figure was associated. Do I need to adjust that if I use 0°C
> as the Standard Temperature?
>
> >> This plots as a straight line passing through (P=0,T=0) with a slope of
> >> (approximately) 0.00366328 atm/K (or atm/°C)
>
> > This is valid for 'ideal' gasses and only if the volume is held constant.
>
> <grin> Understood, but I'm such a rank beginner that these are exactly
> the conditions I'm struggling to establish as a baseline...
>
> > But in a lot of thermodynamics you have to consider a change in the
> > (n/V) term. Then it gets a bit more complicated (but not too bad).
>
> I kinda wondered about that, and I decided that I'd better wrap my head
> around the most simple case first - then add complications as necessary.
>
> > For a fixed mass of gas, we can get a couple of different formulas
> > depending on what process you're interested in.
> >
> > For constant volume:
> > T1/T2 = P1/P2 (this is what you have above)
> >
> > For constant temperature:
> > V1/V2 = P2/P1 (PV= K )
> >
> > Both of the above however require that you add/remove heat as either T
> > or V changes.
>
> So far so good. In what actually I'm working on, neither the volume nor
> the temperature will be constant - but examining the beast with a
> constant volume assumed seems like a good starting point.
>
> > For the case of expansion or compression where there is little time for
> > heat to be transferred in/out, (i.e. the process is adiabatic), we have:
> >
> > PV^y = K
>
> Ah - you've just touched on one of the really big holes in my mental
> model: time. I'm a long way (I think) from incorporating a t variable
> into the process. Methinks I'm going to spend a fair amount of time
> learning heat transfer basics to satisfy that need.
>
> > Where y is the ratio of specific heats (1.4 for air, 1.66 for monoatomic
> > gases and 1.3 for steam). You can combine this with the ideal gas law
> > (PV=nRT) and find the temperature change during compression/expansion as
> > well as volume changes. Substitute P=nRT/V into the above and you get:
> >
> > nRTV^(y-1) = K
> > yielding
> > T1/T2 = (V2/V1)^(y-1)
> >
> > Or substituting V=nRT/P, we get
> > T1/T2 = (P2/P1)^(1-y)/y
>
> Hmm - forewarned is forearmed. This looks like Good Stuff so I've filed
> a copy of your response for future reference. For the moment I'm going
> to stick with dry air or pure water for modeling, although I'm beginning
> to suspect that air will be of decreasing interest.
Just a comment but if you're working with steam the "right" way to go
about it is to get a set of steam tables and work from them. When I was
at Georgia Tech we had a full semester of doing nothing but working with
the steam tables. That was going on 40 years ago though and I've
forgotten most of it.
The "Bible" is Keenan and Keyes--Amazon has used copies of older
editions for as little as four bucks and shipping. Wark's
thermodynamics text also has a usable set IIRC and they've got those
used for around a buck.
There are also online calculators (google "steam tables" and you'll find
a bunch of them) and there's software available but it's not cheap.
Oh, and there's a very very short animation at
<http://www.ecourses.ou.edu/cgi-bin/view_anime.cgi?
file=th020403f.swf&course=th&chap_sec.4> tht I think you might find
helpful--it shows (in metric) the deviation from the ideal gas law at
various points on the PV diagram for water.
Posted by Morris Dovey on December 25, 2010, 4:17 pm
On 12/24/2010 7:09 PM, J. Clarke wrote:
> Just a comment but if you're working with steam the "right" way to go
> about it is to get a set of steam tables and work from them. When I was
> at Georgia Tech we had a full semester of doing nothing but working with
> the steam tables. That was going on 40 years ago though and I've
> forgotten most of it.
Um, yeah - I know how that works (except in my case classes were even
farther back). This stuff is all new to me, so there isn't anything to
refresh.
I have links to more tabular data than I really know what to do with.
What (I think) seems to be most useful are formulas that, at least
approximately, match the tabular data so I can get a gut feel for what
happens and produce an (evolving) software model.
> The "Bible" is Keenan and Keyes--Amazon has used copies of older
> editions for as little as four bucks and shipping. Wark's
> thermodynamics text also has a usable set IIRC and they've got those
> used for around a buck.
I just finished ordering both.
> There are also online calculators (google "steam tables" and you'll find
> a bunch of them) and there's software available but it's not cheap.
Already DAGS and have downloaded PDF versions of some tables. I haven't
found any software yet to do the simulation I want. I've already figured
out that even my own home grown software is going to be fairly expensive
in terms of non-dollar resources required.
> Oh, and there's a very very short animation at
> <http://www.ecourses.ou.edu/cgi-bin/view_anime.cgi?
> file=th020403f.swf&course=th&chap_sec.4> tht I think you might find
> helpful--it shows (in metric) the deviation from the ideal gas law at
> various points on the PV diagram for water.
I've bookmarked it. Thank you - I hadn't seen the deviation portrayal
before.
John, whether you've recognized it or not, you've provided some very
helpful input over a fair number of years - and I don't think I've ever
thanked you properly. Many thanks!
It was your commentary (in r.w) on how poorly your neighbors' solar
panels had held up that ultimately led to mine growing a tougher skin so
they'd last longer. It did take me a while to figure out how I wanted to
go about it, but you can see the result of your influence in the bottom
photo at the link in my sig. :)
--
Morris Dovey
http://www.iedu.com/DeSoto/SC_Madison/
XML site map
> On 1/1/2011 1:43 PM, daestrom wrote:
> > On 12/31/2010 12:47 PM, Morris Dovey wrote:
>
> >> The challenge appears to be allowing (and controlling) the expansion in
> >> such a way that the water remains fluid, and leveraging the high
> >> pressure / low expansion efficiently in the neighborhood of the critical
> >> temperature.
> >>
> >> It seems like it should be possible - and there may be some interesting
> >> solar possibilities if it can be done...
> >
> > If you let it expand enough to change phase, then you can *really* boost
> > the power output. Expanding steam and 'compressing' only liquid water
> > yields a lot of net work. :-)
>
> Ok. I think that's easily managed. I suppose I shouldn't be surprised
> that this part of the pump project now appears headed almost directly
> toward a scaled-up and slightly-modified version of Sno's "pop-pop" engine.
>
> > Problem is, it's been done to death. That's a steam engine pure and
> > simple (expand steam in a cylinder/turbine, 'compress' water in a
> > feed-pump).
>
> Then so be it. The way it's shaping up, the "compression" mechanism will
> probably be a a pump output column/standpipe arrangement.
>
> I don't particularly mind that it's been done to death. If I could find
> a combined engine/pump design that could be driven with solar heat and
> that could be built in a third world bicycle shop for under US$00, I
> could skip this entire exercise and remain blissfully ignorant.
>
> I've probably become over-sensitized, but every news report telling
> about crisis conditions in just about any underdeveloped area seems to
> point to non-availability of water as at least a primary factor - and
> it's not that there isn't any, it's simply in the wrong place - and the
> folks with the problems lack the means to get it.
>
> "Steam Tables (English Units)" by Keyes et al arrived yesterday
> afternoon, and I've been immersed in the appendix a good part of the
> time since. I'm in the process of turning "The Fundamental Equation"
> (Helmholtz free energy) into a trio of C subfunctions - and, as usual, I
> can say that I now know even /more/ that I don't understand. :)
>
> Kinda hoping that Wark's "Thermodynamics" shows up soon to help me
> better understand what I'm attempting...