Interest in Formula for Calculating Alloy Density Still Keen

Alistar writes

Dear Dr. Ron,

Can you send me the answer to your question of 14th Feb. 2005, which follows;

If the density of silver is 10.5 g/cc and the density of tin is 7.31 g/cc. What is the density of an alloy of 96% tin/4% silver.

Hint: The answer is not obtained by multiplying the densities by the percentages and adding together. This question requires thinking about the definition of density. Out of 150 people given this question on a certification test, only 2 got it right.

The correct answer is 7.40 g/cc (7.399927 exactly) Bob Jarrett was the first one with a correct answer. If anyone wants the technique explained or a copy of an Excel spreadsheet that perfroms these calculations send me an email (rlasky@indium.com)

Thanks in advance,

Alistair

Dear Alistair,

An easy way to understand this (proposed by Bob Jarrett) is to consider the 96% tin, 4 % silver example.

Lets assume I have 1 g of this alloy, 0.96 g is tin and 0.04 g is silver.

The volume of the tin is 0.96 g/7.31g/cc = 0.131327cc

The volume of the silver is 0.04g/10.5g/cc = 0.00381cc

So 1 g of the alloy has a volume of 0.131327 + 0.00381 cc = 0.135137 cc

Hence it's density is 1g/0.135137cc = 7.39989g/cc

The general formula is:

1/Da = x/D1 + y/D2 + z/D3

Da = density of final alloy

D1 = density of metal 1, x = mass fraction of metal 1

same for metals 2 and 3

Formula continues for more than 3 metals.

I have developed an Excel spreadsheet (shown calculating the density of SAC 305) that calculates density automatically. If anyone wants a copy, send me an email at rlasky@indium.com.

Cheers

Dr Ron

Posted by Dr. Ron Lasky on August 16th, 2006 at 8:09 PM

Comments (add your comment)

  1. karthick prabhu.c:

    its a very nice formula but still i have some doubts... will you please send me the exact formulae for calculating...the alloy density.. for various metal compositions...
    thanking you
    in advance

  2. SWAPAN KUMAR BOSE:

    Dear Sir,
    This formula is very good and useful.Will you pl. send me a copy of Exel Spreadsheed that calculates density automatically devoloped by you.

    Thanking You in advance.

    With Regards,

    Skb.

  3. Ajay Pareek:

    DearSir, This fourmula is very good and useful,plese send me a copy . Thanking you

  4. Dr. Perumal:

    Thanks for giiving us the information about density calculations. Could you send us the Excel spreadsheet.

    Thanks in advance.

  5. student:

    Dear sir

    thanks for this formular.However, could you send all formation about density for me please.

    thanks.

  6. Gerry Chen:

    Good idea! could you send me the excel spreadsheet.Thanks.

  7. Rochelle:

    Sir,

    Thank you for the information. Kindly send the excel file.

    Thanks a lot

  8. John Teets:

    Please send me a copy of the spreadsheet for the density calculator. We manufacture fine diameter wire using precious metals and this will be a great help with alloys that are not standard. Thanks.

  9. Tarek El-Ashram:

    Thank you for this method of calculating the density of an alloy, but what about if there is intermetallics or vacancies.

  10. T.P.yadav:

    Please send me the density of

    ZrFe2 alloys

    thank you

  11. Tommy Fan :

    Dear Dr. Lasky,
    Can you also give me the Excel spreadsheet of the calculating the density

    Thank you Tommy Fan

  12. John:

    Hopefully this post works. Trying for the fifth time this time in a different browser.

    This is from density = mass / volume.

    First find the volume of each item.
    D = M / V
    10.5 = .04 / V
    V silver = .0038095

    D = M / V
    7.31 = .96 / V
    V tin = .13133

    Now find the combined density
    D= M / V
    D= M1+M2 / V1+V2
    D= .04+.96 / .0038095+.13133
    D= 7.399

    When you have 2 components, the combined density will be between the individual components density. You can use as many components as you like. You can use whatever units for measurement you like, but they all have to match.

  13. Ramesh:

    Dear Sir,
    Is there a possibility to obtain a copy of the excel sheet that calculates density automatically.

    Thank You in advance.

    With Regards,
    Ramesh

  14. Edward:

    Dear Sir,

    Thank you for the equations, but I have a question, what if after alloying they form a different phase? Will this equation still apply?

    Also, could you still send me a copy of the excel spread sheet or any information you have on densities of alloys?

    Thanks in advance.

    Regards,
    Edward

  15. BELUR RAGAVAN RAVI:

    DEAR SIR,
    GOOD DAY. I SHALL BE MUCH OBLIGED IF YOU WILL SEND ME A COPY OF EXCEL SPREAD SHEET AT YOUR EARLIEST CONVENIENCE. I THANK YOU FOR YOUR SERVICE BY PROVIDING SIMPLE METHOD TO CALCULATE ALLOY DENSITY.
    THANKING YOU AGAIN.
    WISH YOU GOOD LUCK FOR EVERY GOOD THING YOU LOVE TO ENJOY.
    KIND REGARDS,
    B.R.RAVI.

  16. carwaterguide.blogspot.com:

    I’m excitedly waiting all the changes in technology and availability of vehicles in the near future!!!

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