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Author Topic: NXT Silver Bullion Gateway Gateway Updates and Information  (Read 12224 times)
Anon136
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March 12, 2014, 10:33:57 PM
 #121

For the smart maths people out there

This chart says http://www.engineeringtoolbox.com/volum-expansion-coefficients-solids-d_1894.html the volumetric thermal expansion coefficient of silver is 58.3 (10-6 m/(m K)) i can only assume they mean m^3 since that is how you would measure volume.

So if i multiply 58.3*0.000001 i get 0.0000583

So silver expands at 0.0000583 meters cubed per meter cubed per kelvin.

Room temperature is about 300 kelvin. The melting point of silver is about 1233 kelvin. So that's a difference of 933 kelvin.

So then i just multiply 0.0000583*933 and get 0.0543939 meters cubed per meter cubed of change.

Ive got to be honest that seems crazy. a 5.5% change in size as it cools? there is no way that can be right.

Its written as a linear expansion coefficient e.g. (m/m K) not (m^3/(m K)), a linear coefficient which is change in length per meter and degree of temperature, volumetric is 3x linear for a solid, but another reference I have says the volumetric expansion coefficient for silver is 54 *10^-6 (m^3/(m K)) AT 20C - I don't think solid to liquid volume change can't be calculated using a constant - sorry.

it doesn't need to be. the only point at which shrinking matters is past the point at which it has transitioned from liquid to solid. as long as its liquid it can flow freely through out the chamber of the mould. so the point at which it becomes solid is the upper bound for what i need to calculate.

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March 12, 2014, 10:35:47 PM
 #122

http://iweb.tntech.edu/murdock/books/bookv3.pdf

#7 under worked examples verifies that you're using the equations right

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March 12, 2014, 10:39:53 PM
 #123

http://iweb.tntech.edu/murdock/books/bookv3.pdf

#7 under worked examples verifies that you're using the equations right

awesome! i can never make heads or tales of fancy math stuff like that. it looks like french to me. i just have to work through the logic in my head Cheesy

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March 12, 2014, 10:49:34 PM
 #124

BUT I don't think solid to liquid volume change can be calculated using a constant - so your 5% may be wrong because you have a 'state change'

yes, the coefficients are not constant, they depend on the temperature and the pressure
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March 12, 2014, 10:54:31 PM
 #125

BUT I don't think solid to liquid volume change can be calculated using a constant - so your 5% may be wrong because you have a 'state change'

yes, the coefficients are not constant, they depend on the temperature and the pressure

ok well that's really going to go out of my league. can any of you smart guys tell me how much the volume would change when cooling from 1234K to 300K?

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March 12, 2014, 10:59:57 PM
 #126

BUT I don't think solid to liquid volume change can be calculated using a constant - so your 5% may be wrong because you have a 'state change'

yes, the coefficients are not constant, they depend on the temperature and the pressure

ok well that's really going to go out of my league. can any of you smart guys tell me how much the volume would change when cooling from 1234K to 300K?

do you plan to cast silver yourself? That is pretty complicated.

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March 12, 2014, 11:01:52 PM
 #127

BUT I don't think solid to liquid volume change can be calculated using a constant - so your 5% may be wrong because you have a 'state change'

yes, the coefficients are not constant, they depend on the temperature and the pressure

ok well that's really going to go out of my league. can any of you smart guys tell me how much the volume would change when cooling from 1234K to 300K?

do you plan to cast silver yourself? That is pretty complicated.

yes i do and yes i know. what we are talking about right now is just part of the complications Cheesy

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March 12, 2014, 11:03:02 PM
 #128

BUT I don't think solid to liquid volume change can be calculated using a constant - so your 5% may be wrong because you have a 'state change'

yes, the coefficients are not constant, they depend on the temperature and the pressure

ok well that's really going to go out of my league. can any of you smart guys tell me how much the volume would change when cooling from 1234K to 300K?


Maybe chanc3r's solid/liquid numbers are the most useful (depending on your accuracy requirements)...
 until someone finds the nonlinear coefficients for silver Smiley


density of solid silver at room temperature = 10.49gcm^-3
density of liquid silver at melting point= 9.320gcm^-3

perhaps this is a simpler - the ratio of the densities will give you a volume change between liquid silver and room temperature solid silver.
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March 12, 2014, 11:07:35 PM
 #129

BUT I don't think solid to liquid volume change can be calculated using a constant - so your 5% may be wrong because you have a 'state change'

yes, the coefficients are not constant, they depend on the temperature and the pressure

ok well that's really going to go out of my league. can any of you smart guys tell me how much the volume would change when cooling from 1234K to 300K?


Maybe chanc3r's solid/liquid numbers are the most useful (depending on your accuracy requirements)...
 until someone finds the nonlinear coefficients for silver Smiley


density of solid silver at room temperature = 10.49gcm^-3
density of liquid silver at melting point= 9.320gcm^-3

perhaps this is a simpler - the ratio of the densities will give you a volume change between liquid silver and room temperature solid silver.


good point. the mean between those values would be a good estimation.

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March 12, 2014, 11:08:06 PM
 #130

BUT I don't think solid to liquid volume change can be calculated using a constant - so your 5% may be wrong because you have a 'state change'

yes, the coefficients are not constant, they depend on the temperature and the pressure

ok well that's really going to go out of my league. can any of you smart guys tell me how much the volume would change when cooling from 1234K to 300K?

do you plan to cast silver yourself? That is pretty complicated.

yes i do and yes i know. what we are talking about right now is just part of the complications Cheesy

I assume that you cast at 1 atm, so the process is roughtly at constant pressure.

For a good approximation, I believe you need to use integral formula with alpha(T)  function of temperature. I don<T know, but some table might exist in the litterature at constant pressure (1 atm). If you have this curve, I dont believe the phase change will do anything because it effect will already be in the curve alpha(T).

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March 12, 2014, 11:09:18 PM
 #131

BUT I don't think solid to liquid volume change can be calculated using a constant - so your 5% may be wrong because you have a 'state change'

yes, the coefficients are not constant, they depend on the temperature and the pressure

ok well that's really going to go out of my league. can any of you smart guys tell me how much the volume would change when cooling from 1234K to 300K?

do you plan to cast silver yourself? That is pretty complicated.

yes i do and yes i know. what we are talking about right now is just part of the complications Cheesy

I assume that you cast at 1 atm, so the process is roughtly at constant pressure.

For a good approximation, I believe you need to use integral formula with alpha(T)  function of temperature. I don<T know, but some table might exist in the litterature at constant pressure (1 atm). If you have this curve, I dont believe the phase change will do anything because it effect will already be in the curve alpha(T).

it doesn't need to be that accurate. its good practice to cast at a little over the denomination anyway.

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Sebastien256
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March 12, 2014, 11:12:56 PM
 #132

BUT I don't think solid to liquid volume change can be calculated using a constant - so your 5% may be wrong because you have a 'state change'

yes, the coefficients are not constant, they depend on the temperature and the pressure

ok well that's really going to go out of my league. can any of you smart guys tell me how much the volume would change when cooling from 1234K to 300K?

do you plan to cast silver yourself? That is pretty complicated.

yes i do and yes i know. what we are talking about right now is just part of the complications Cheesy

I assume that you cast at 1 atm, so the process is roughtly at constant pressure.

For a good approximation, I believe you need to use integral formula with alpha(T)  function of temperature. I don<T know, but some table might exist in the litterature at constant pressure (1 atm). If you have this curve, I dont believe the phase change will do anything because it effect will already be in the curve alpha(T).

it doesn't need to be that accurate. its good practice to cast at a little over the denomination anyway.

Depending on accuracy you don'T have to use integral, but only do stair approximation of the curve. and compute 100*dV/V for a certain number of dT interval. After which you sum up each 100*dV/V computed.

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March 12, 2014, 11:13:25 PM
 #133

NXT Logo and silver -the ideas are unlimited. Great project Anon.

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March 12, 2014, 11:14:56 PM
 #134

BUT I don't think solid to liquid volume change can be calculated using a constant - so your 5% may be wrong because you have a 'state change'

yes, the coefficients are not constant, they depend on the temperature and the pressure

ok well that's really going to go out of my league. can any of you smart guys tell me how much the volume would change when cooling from 1234K to 300K?


Maybe chanc3r's solid/liquid numbers are the most useful (depending on your accuracy requirements)...
 until someone finds the nonlinear coefficients for silver Smiley


density of solid silver at room temperature = 10.49gcm^-3
density of liquid silver at melting point= 9.320gcm^-3

perhaps this is a simpler - the ratio of the densities will give you a volume change between liquid silver and room temperature solid silver.


good point. the mean between those values would be a good estimation.

if just calculating with an example, 1000 g of silver:

liquid :  V = 1000 g / 9.3 g/cm3 =  107.5268 cm3
solid:    V = 1000 g / 10.49 g/cm3 = 95.328 cm3

Volume change  X %  is broadly 11.3 %.  
 (if you need more accurate, then it needs  equation Smiley
     V1 - (V1/100*X) = V2

  
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March 12, 2014, 11:15:55 PM
 #135

anon: I'm pretty sure your calculation of 5.5% difference is correct, you used the formulas and values correctly.
a temperature difference of about 900 degrees is pretty severe, I think a shrinking of 5% is absolutely possible.
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March 12, 2014, 11:32:24 PM
 #136

anon: I'm pretty sure your calculation of 5.5% difference is correct, you used the formulas and values correctly.
a temperature difference of about 900 degrees is pretty severe, I think a shrinking of 5% is absolutely possible.

if there happens that liquid -> solid change, then the volume change is more (11.3 %),
according to those densities http://en.wikipedia.org/wiki/Silver

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March 13, 2014, 12:05:37 AM
 #137

anon: I'm pretty sure your calculation of 5.5% difference is correct, you used the formulas and values correctly.
a temperature difference of about 900 degrees is pretty severe, I think a shrinking of 5% is absolutely possible.

maybe anon can start by that and adjusting by experience. If anon cast many silver bar, then It only take a couple adjustment from experiment to make it right. I don't know. Is that what you plan anon?
Or you want to be right the first time?

You can use the newton method or the bissection method to adjust rapidly your experimental guess each time given the results of your previous casting.  

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March 13, 2014, 12:19:33 AM
 #138

anon: I'm pretty sure your calculation of 5.5% difference is correct, you used the formulas and values correctly.
a temperature difference of about 900 degrees is pretty severe, I think a shrinking of 5% is absolutely possible.

maybe anon can start by that and adjusting by experience. If anon cast many silver bar, then It only take a couple adjustment from experiment to make it right. I don't know. Is that what you plan anon?
Or you want to be right the first time?

You can use the newton method or the bissection method to adjust rapidly your experimental guess each time given the results of your previous casting.  

yes its going to involve experimentation. that's inevitable. as complicated as this all sounds one has to consider additionally that the mould its self will be expanding and contracting with the heat. i hope my customers will be patient with me if my earlier bars come in at under 10 troy ounces. i will of course re-pour them for free when i get it perfect at some point in the future.

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March 13, 2014, 12:20:54 AM
 #139

anon: I'm pretty sure your calculation of 5.5% difference is correct, you used the formulas and values correctly.
a temperature difference of about 900 degrees is pretty severe, I think a shrinking of 5% is absolutely possible.

maybe anon can start by that and adjusting by experience. If anon cast many silver bar, then It only take a couple adjustment from experiment to make it right. I don't know. Is that what you plan anon?
Or you want to be right the first time?

You can use the newton method or the bissection method to adjust rapidly your experimental guess each time given the results of your previous casting.  

yes its going to involve experimentation. that's inevitable. as complicated as this all sounds one has to consider additionally that the mould its self will be expanding and contracting with the heat. i hope my customers will be patient with me if my earlier bars come in at under 10 troy ounces. i will of course re-pour them for free when i get it perfect at some point in the future.

Do you have some experience in casting? or some people around you know that science? Casting at 1200-1300K is very dangerous.

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March 13, 2014, 12:41:58 AM
 #140

anon: I'm pretty sure your calculation of 5.5% difference is correct, you used the formulas and values correctly.
a temperature difference of about 900 degrees is pretty severe, I think a shrinking of 5% is absolutely possible.

maybe anon can start by that and adjusting by experience. If anon cast many silver bar, then It only take a couple adjustment from experiment to make it right. I don't know. Is that what you plan anon?
Or you want to be right the first time?

You can use the newton method or the bissection method to adjust rapidly your experimental guess each time given the results of your previous casting.  

yes its going to involve experimentation. that's inevitable. as complicated as this all sounds one has to consider additionally that the mould its self will be expanding and contracting with the heat. i hope my customers will be patient with me if my earlier bars come in at under 10 troy ounces. i will of course re-pour them for free when i get it perfect at some point in the future.

Do you have some experience in casting? or some people around you know that science? Casting at 1200-1300K is very dangerous.

no i dont not have any experience. of course that can be said for everyone who does at some point in their life. i am working with newliberty.

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