# The Naked Scientists Forum

### Author Topic: What is the expansion ratio of liquid methane?  (Read 8284 times)

#### Lab Rat

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##### What is the expansion ratio of liquid methane?
« on: 07/10/2012 20:08:41 »
What is the generally accepted expansion ratio of liquid methane?
I have looked on the internet, but I have found only two places that gave the same value.  Here are the values I've found:
1:650
>851
1:578
1:627
1:627
« Last Edit: 08/10/2012 21:38:01 by chris »

#### Bored chemist

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##### Re: Expansion Ratio of Liquid Methane
« Reply #1 on: 07/10/2012 21:59:28 »
It will depend on how warm you get the gas.

#### damocles

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##### Re: Expansion Ratio of Liquid Methane
« Reply #2 on: 07/10/2012 23:59:19 »
For this type of information, go to the NIST Webbook. I have the following for methane density:

Liquid at 111.67 K (normal boiling point) d = 422.36 kg/m^3
Gas at 111.67 K d = 1.8164 kg/m^3
Gas at 273 K d = 0.718 kg/m^3 (interpolation)
Gas at 298 K d = 0.657 kg/m^3 (interpolation)

Expansion factors: gas at boiling point relative to liquid at boiling point -- 233
gas at 0 °C relative to liquid at boiling point -- 588
gas at 25°C relative to liquid at boiling point -- 643

The 850 plus figure is probably for gas at an ambient temperature against solid at 77 K (liquid nitrogen temperature -- for which I do not have data)

#### Lab Rat

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##### Re: Expansion Ratio of Liquid Methane
« Reply #3 on: 08/10/2012 14:19:29 »
It will depend on how warm you get the gas.
I guess I should have been more specific.  What would its expansion ratio be at room temperature?

#### damocles

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##### Re: Expansion Ratio of Liquid Methane
« Reply #4 on: 08/10/2012 21:36:31 »
It will depend on how warm you get the gas.
I guess I should have been more specific.  What would its expansion ratio be at room temperature?

I will be very specific -- there is no such thing as an expansion ratio at room temperature because liquid methane cannot exist at room temperature -- the critical temperature of methane is –83 °C

#### evan_au

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##### Re: What is the expansion ratio of liquid methane?
« Reply #5 on: 09/10/2012 10:36:04 »
If you assume the molecules have zero volume, then it acts as a "perfect gas" and will follow Charles' Law (http://en.wikipedia.org/wiki/Charles%27_law).

This means that its volume will shrink from "Gas at 298 K d = 0.657 kg/m^3" down to zero volume at absolute zero (0K=-273.16C).

Of course, it stops acting as an ideal gas when you approach the boiling point (111K).

Van der Waals produced a more accurate relationship which takes into account the finite volume of the molecule, and the attraction between the molecules (http://en.wikipedia.org/wiki/Van_der_Waals_equation). This gives results which are more accurate than a "straight line" extrapolation to absolute zero.

Van der Waals' formula requires two parameters:
• a is a measure for the attraction between the particles, and
• b is the average volume excluded from v by a particle

However, I am having trouble finding the a & b values for methane - could an experienced chemist show where to find these quantities, please?

#### damocles

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##### Re: What is the expansion ratio of liquid methane?
« Reply #6 on: 09/10/2012 10:48:51 »
Evan, the van der Waals equation is only an approximation, and it cannot address the question of the expansion ratio of liquid methane, as required by the OP. It is possible to fit the vdW constants from the critical parameters of a fluid, or from the liquid density (to give the molar volume parameter) and the normal boiling point (to give the anergy of attraction parameter);

wikipedia has a page of vdW constants at http://en.wikipedia.org/wiki/Van_der_Waals_constants_(data_page); it includes methane.

But there is a complete tabulation of properties of both liquid and gaseous methane at
webbook.nist.gov/chemistry/fluid

#### Lab Rat

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##### Re: Expansion Ratio of Liquid Methane
« Reply #7 on: 09/10/2012 14:10:58 »
It will depend on how warm you get the gas.
I guess I should have been more specific.  What would its expansion ratio be at room temperature?

I will be very specific -- there is no such thing as an expansion ratio at room temperature because liquid methane cannot exist at room temperature -- the critical temperature of methane is –83 °C
Sorry, just another case of me not explaining myself well (I knew that it can't be a gas a room temperature).  I meant:
What is its expansion ratio going from a liquid at its critical temperature of -83° C to a gas at room temperature (20° C)?  (How much will it expand going from a liquid to a gas at said temperatures?)
Thanks for all the info so far, damocles.  It has been a big help.
« Last Edit: 09/10/2012 14:21:16 by Lab Rat »

#### BioChemSFC

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##### Re: Expansion Ratio of Liquid Methane
« Reply #8 on: 18/10/2012 02:06:42 »
It will depend on how warm you get the gas.

Yes this (temp of gas) is the factor that would have a significant influence on the ratio. Liquid density does vary with temp as well but in such a small amount that it is eclipsed by the volume effect of gas temp (unless the volume was limited by container). the ideal gas equation PV=nRT show temp linearly effects volume.  If you want the ratio at STD gas conditions then don't ask it here just look it up. I bet it's on wikipedia. I think you can figure this one out given the density of liquid methane and the density of gaseous methane at standard conditions. Sorry I don't do free homework.

#### Bored chemist

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##### Re: What is the expansion ratio of liquid methane?
« Reply #9 on: 18/10/2012 19:13:21 »
The density of methane at NTP is 0.668 kg/m^3
http://www.engineeringtoolbox.com/gas-density-d_158.html
the density of liquid methane is 422,700 kg/m^3

Ratio is 638

Unless you are in a position to ensure that the atmospheric pressure is exactly one standard atmosphere then any further complications are pretty pointless.

#### BioChemSFC

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##### Re: What is the expansion ratio of liquid methane?
« Reply #10 on: 26/10/2012 10:51:12 »
The density of methane at NTP is 0.668 kg/m^3
the density of liquid methane is 422,700 kg/m^3

Ratio is 638

Unless you are in a position to ensure that the atmospheric pressure is exactly one standard atmosphere then any further complications are pretty pointless.

Incorrect. This statement is counter intuitive. Your value of the density of methane at NTP is totally reliant on standard conditions. So your calcuations are relying on the gas being at standard temp and pressure. So without thinking about it you are assuming that you ARE in the position to ensure these varibles.  If you are not at standard conditions for NTP then the other variables are far from pointless. They dictate the volume. They are the determining factor. These are not "complications" but rather the factors that dictate the ratio. Recall PV=nRT.

#### Bored chemist

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##### Re: What is the expansion ratio of liquid methane?
« Reply #11 on: 26/10/2012 18:36:14 »
You do know that PV=nRT isn't actually true, don't you?
The deviations are fairly small. They are not worth worrying about because they make less difference to the true value than normal variation in atmospheric pressure. That was my point.
Also, I fairly clearly chose the value from that web site at NTP (because it was specified in the 3rd post in the thread) rather than STP, so the idea that I'm relying on it being at STP is absurd.

#### syhprum

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##### Re: What is the expansion ratio of liquid methane?
« Reply #12 on: 15/11/2012 08:12:41 »
"the density of liquid methane is 422,700 kg/m^3"
I think perhaps a decimal point was intended not a comma !

#### damocles

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##### Re: What is the expansion ratio of liquid methane?
« Reply #13 on: 15/11/2012 13:24:45 »

"the density of liquid methane is 422,700 kg/m^3"
I think perhaps a decimal point was intended not a comma !

BC is simply being a good European and using a continental comma for a decimal point (as is standard outside anglophone countries)

#### Bored chemist

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##### Re: What is the expansion ratio of liquid methane?
« Reply #14 on: 15/11/2012 19:21:55 »
Much as I'd like to pretend that that is true I have to admit it was a typo.

#### The Naked Scientists Forum

##### Re: What is the expansion ratio of liquid methane?
« Reply #14 on: 15/11/2012 19:21:55 »