Answer :
Answer:
The required tensile strength is 175.13 MPa.
Explanation:
Given that,
Tensile strength(MPa) Number Average Molecular weight(g/mol)
36 30,000
150 50,000
First we need to find out [tex]TS_\infty[/tex]tensile strength at infinity molecular weight.
The formula of tensile strength
[tex]TS=TS_\infty-\frac{A}{ M_n}[/tex]
TS is tensile strength,[tex]TS_\infty[/tex] at infinity molecular weight, [tex]M_n[/tex] is molecular weight and A is constant.
Now substituting [tex]TS=36[/tex] and [tex]M_n=30,000[/tex]
[tex]36=TS_\infty-\frac{A}{30,000}[/tex]
[tex]\Rightarrow TS_\infty=36+\frac{A}{30,000}[/tex] ........(1)
Now substituting [tex]TS=150[/tex] and [tex]M_n=50,000[/tex]
[tex]150=TS_\infty-\frac{A}{50,000}[/tex]
[tex]\Rightarrow TS_\infty=150+\frac{A}{50,000}[/tex] ......(2)
Subtract (1) from (2)
[tex]TS_\infty-TS_\infty=150+\frac{A}{50,000}-36-\frac{A}{30,000}[/tex]
[tex]\Rightarrow150+\frac{A}{50,000}-36-\frac{A}{30,000}=0[/tex]
[tex]\Rightarrow \frac{A}{30,000}-\frac{A}{50,000}=150-36[/tex]
[tex]\Rightarrow \frac{5A-3A}{1,50,000}=114[/tex]
[tex]\Rightarrow \frac{2A}{1,50,000}=114[/tex]
[tex]\Rightarrow A=\frac{1,50,000 \times114}{2}[/tex]
[tex]\Rightarrow A=8,550,000[/tex]
Putting the value of A in equation (1)
[tex]TS_\infty=36+\frac{8,550,000}{30,000}[/tex]
=361 MPa
Now to find the tensile strength at a number average molecular weight of 46,000 g/mol , Putting the value [tex]TS_\infty[/tex], TS and A
[tex]\therefore TS=361-\frac{8,550,000}{ 46,000}[/tex]
= 175.13 MPa
The required tensile strength is 175.13 MPa.
