[Gasification] sidebar Ideal Gas Law for engineering - was: Re: Benefits of boosting compression ratio

[Daniel Chisholm]

On Wed, Mar 2, 2011 at 14:11, Toby Seiler <seilertechco at yahoo.com> wrote:

> Mark, Daniel C., list,
>
> OK I admit that I'm lost when I get to "mole" in the ideal gas law.  (A
> mole is a furry creature my dog brings up on the porch to chew up.)
>

Yeah moles can throw one for a loop, I think it is the Chemists' way of
keeping all the fun stuff to themselves.

In engineering applications the equation for the ideal gas law is expressed
a bit differently. Even though it means exactly the same thing, the
quantities that it uses are more relevant to engineering approaches:

P = rho * R * T

where P is the pressure, rho is the density of the gas, R is the gas
constant *of that gas* (not the Universal Gas Constant), and T is the
temperature (in an absolute temp. scale i.e Kelvin or Rankine).

These quantities are chosen because for many engineering problems it is more
convenient to work with the density of a gas than with the volume of the gas
and the number of moles of gas in that volume (we don't ordinarily control
or measure the number of moles)

This equation is valid in any consistent set of units.  While I have nothing
against Imperial or US Customary units and in fact use them quite freely for
many things, there is a big trap waiting for the unwary (such as me!) with
the difference between "pounds-mass" and "pounds-force".  This is the reason
that you often see "w/g" or "w/32" factors in equations, the "g" or
"32ft/sec/sec", it is the gravitation acceleration term used to convert
pounds-mass to pounds-force.  Frankly since I didn't learn things that way
and am worried about making a mistake I prefer to switch into SI units for
my physics or engineering calculations and then perhaps switch back to
Imperial for building things.

In SI units we have:

P = pressure, in Pascals (which is Newtons per square metre).  FYI standard
sea level atmospheric pressure is 101,325Pa which is conveniently close to
100,000Pa that that is usually used.  If you are more comfortable thinking
in PSI (like I am for some things) you can convert PSI to Pascals by
multiplying by 101325/14.69.  If you prefer approximations there are about
7000 Pascals per PSI.  And when dealing with lower pressures such as from
fans and blowers, one inch of water column is very close to 250 Pascals

rho = density, in kilograms per cubic metre.  Air has a density of about
1.22kg/m3 at a temperature of 15C.  I find it very convenient since I can
visualize how big a cubic metre is and I can also visualize how much a
kilogram is.

R = individual gas constant.  For air it is 286.9 Joules/kg/K.  BTW I didn't
know that I had to look it up - see
http://www.engineeringtoolbox.com/individual-universal-gas-constant-d_588.htmlfor
more info.  Gases of interest to us are mixtures of water vapour,
oxygen, nitrogen, carbon monoxide, carbon dioxide and hydrogen.  The gas
constant of mixtures of gases is quite straightforward, you use multiply
"volume percent" of each gas by its individual gas constant, and then sum
all of these contributions.

T = temperature in Kelvin.  Freezing (0C, 32F) is 273 K, "standard temp"
(15C , 59F) is 288K.  Typical warm air temps are conveniently about 300K
(which is 27C or 80F).


-- 
- Daniel
Fredericton, NB  Canada
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