Answer:
Explanation:
The question can be well structured in a table format as illustrated below:
Tensile Strength (MPa) Number- Average Molecular Weight (g/mol)
82 12,700
156 28,500
The tensile strength and number-average molecular weight for two polyethylene materials given above.
Estimate the number-average molecular weight that is required to give a tensile strength required above. Using the data given find TS (infinity) in MPa.
<u>SOLUTION:</u>
We know that :
where;
= Tensile Strength
= Tensile Strength (Infinity)
= Number- Average Molecular Weight (g/mol)
SO;
From equation (1) ; collecting the like terms; we have :
From equation (2) ; we have:
So;
Then;
Solving by L.C.M
By cross multiplying ; we have:
Collecting like terms ; we have
Dividing both sides by 15800:
A = 1695208.861
From equation (1);
Replacing A = 1695208.861 in the above equation; we have:
From equation(2);
Replacing A = 1695208.861 in the above equation; we have:
We are to also estimate the number- average molecular weight that is required to give a tensile strength required above.
If the Tensile Strength (MPa) is 82 MPa
Definitely the average molecular weight will be = 12,700 g/mol
If the Tensile Strength (MPa) is 156 MPa
Definitely the average molecular weight will be = 28,500 g/mol
But;
Let us assume that the Tensile Strength (MPa) = 181 MPa for example.
Using the same formula:
Then:
Collecting like terms ; we have:
1695208.861= 34.481
Dividing both sides by 34.481; we have:
=
