Insane multivariable problem with alloys and metal properties.

[mindcoremedia]

The simplest I can explain it is:

We have to theoretically mix 2 or 3 alloys that have the same properties of silver listed below

1. Weight per cubic cm
2. Diamagnetic repelling force

Just can't figure out how to calculate it.
___________________


My partner and I were assigned a project. We came up with the idea to create an equation that would satisfy an ultimate condition of an alloy of metals having the same weight per volume, and diamagnetic value as the original pure metal element.

I think we bit off more than we can chew. We need your help guys.

Our main idea was to create a theoretical alloy from 2-3 metals that have the same 2 values mentioned above as silver

Here are the values we are working with:

Bismuth:
9.808 gram per cubic cm
-16.6 χm [× 10−5 (SI units)] diamagnetic value

Silver:
10.5 gram per cubic cm
-2.6 χm [× 10−5 (SI units)] diamagnetic value

Lead:
11.342 grams per cubic cm
-1.8 χm [× 10−5 (SI units)] diamagnetic value

Copper
8.94 grams per cubic centimeter
-1.0 χm [× 10−5 (SI units)] diamagnetic value

Diamagnetic values are shown in negatives however bismuth has over 6x the diamagnetic properties of silver.

If anyone could help with this it would be amazing. We are totally lost. Thanks guys/ladies.

 

[Deleted member 4993]

The simplest I can explain it is:

We have to theoretically mix 2 or 3 alloys that have the same properties of silver listed below

1. Weight per cubic cm
2. Diamagnetic repelling force

Just can't figure out how to calculate it.
___________________


My partner and I were assigned a project. We came up with the idea to create an equation that would satisfy an ultimate condition of an alloy of metals having the same weight per volume, and diamagnetic value as the original pure metal element.

I think we bit off more than we can chew. We need your help guys.

Our main idea was to create a theoretical alloy from 2-3 metals that have the same 2 values mentioned above as silver

Here are the values we are working with:

Bismuth:
9.808 gram per cubic cm
-16.6 χm [× 10−5 (SI units)] diamagnetic value

Silver:
10.5 gram per cubic cm
-2.6 χm [× 10−5 (SI units)] diamagnetic value

Lead:
11.342 grams per cubic cm
-1.8 χm [× 10−5 (SI units)] diamagnetic value

Copper
8.94 grams per cubic centimeter
-1.0 χm [× 10−5 (SI units)] diamagnetic value

Diamagnetic values are shown in negatives however bismuth has over 6x the diamagnetic properties of silver.

If anyone could help with this it would be amazing. We are totally lost. Thanks guys/ladies.

Please show us what you have tried and exactly where you are stuck.

Please follow the rules of posting in this forum, as enunciated at:

https://www.freemathhelp.com/forum/threads/read-before-posting.109846/#post-486520

Please share your work/thoughts about this assignment.

 

[mindcoremedia]

I basically need to figure out how to another create an alloy or layered metal that has the same water displacement, weight and speed down a magnetic track at a 45 degree angle. (Diamagnetic force).

If I'm able to calculate it I get an a on the assignment. If I'm able to create the metal I get an a for the semester. Not allowed to electroplate the metal due to ethical concerns.


Here is what I have so far, I'm not sure if I'm moving in the right direction or not.

Would this be appropriate for the answer I'm seeking? I still have no idea how to continue after this.

9.808 g. * x = a

8.94 g. * y = b

11.342 g. * z = c
______________________
(9.808 grams * x + 8.94 grams * y + 11.342 grams * z) / 3 = 10.5 grams

While

(a * 16.6) + (b * 1) + (c * 1.8) = 2.6

 

[HallsofIvy]

Taking x and y to be the proportions of each of the two metals in the alloy, \(\displaystyle d_1\) and \(\displaystyle d_2\) the densities of the two chosen metals, and \(\displaystyle m_1\) and \(\displaystyle m_2\) the diamagnetic values, you want:
x+ y= 1
\(\displaystyle d_1x+ d_2y= 10.5\) and
\(\displaystyle m_1x+ m_2y= -0.000026\)
You need to choose the two metals, so \(\displaystyle d_1\), \(\displaystyle m_1\), \(\displaystyle d_2\), and \(\displaystyle d_2\), and x and y to satisfy those equations. Or course such values might not exist!

 

[Dr.Peterson]

Before doing this, since you're doing actual metallurgy and not mere math, I'd want to confirm that diamagnetic susceptibility of elements combines linearly in an alloy. I did find this, which suggests both that that is merely "assumed", and that it may be valid: https://www.sciencedirect.com/science/article/abs/pii/0304885386900302

 

[Deleted member 4993]

The simplest I can explain it is:

We have to theoretically mix 2 or 3 alloys that have the same properties of silver listed below

1. Weight per cubic cm
2. Diamagnetic repelling force

Just can't figure out how to calculate it.
___________________


My partner and I were assigned a project. We came up with the idea to create an equation that would satisfy an ultimate condition of an alloy of metals having the same weight per volume, and diamagnetic value as the original pure metal element.

I think we bit off more than we can chew. We need your help guys.

Our main idea was to create a theoretical alloy from 2-3 metals that have the same 2 values mentioned above as silver

Here are the values we are working with:

Bismuth:
9.808 gram per cubic cm
-16.6 χm [× 10−5 (SI units)] diamagnetic value

Silver:
10.5 gram per cubic cm
-2.6 χm [× 10−5 (SI units)] diamagnetic value

Lead:
11.342 grams per cubic cm
-1.8 χm [× 10−5 (SI units)] diamagnetic value

Copper
8.94 grams per cubic centimeter
-1.0 χm [× 10−5 (SI units)] diamagnetic value

Diamagnetic values are shown in negatives however bismuth has over 6x the diamagnetic properties of silver.

If anyone could help with this it would be amazing. We are totally lost. Thanks guys/ladies.

Let us assume that the alloy is made with two materials:

metal 1 with density r₁, diamagnetic value d₁ and "volume fraction" (v₁), and

metal 2 with density r₂, diamagnetic value d₂ and "volume fraction" (v₂)

where v₁ + v₂ =1 .....................................(1)

the density of the alloy (r_a):

r_a = v₁ * r₁ + v₂ * r₂................(2)

Diamagnetic property similarly can be calculated:

the diamagnetic property of the alloy (d_a):

d_a = v₁ * d₁ + v₂ * d₂...........(3)

now continue.........