GATE (TF) Textile 2012 Question Paper Solution | GATE/2012/TF/26

Question 26 (Textile Engineering & Fibre Science)

The density of a given polyester filament sample is 1.38 g/cm3. Consider the density of fully crystalline polyester at 1.455 g/cm3 and that of fully amorphous polyester as 1.335 g/cm3. The percent crystalline of the sample is _____________

Answer / Solution

Given in the question-

Density of fibre(\rho)=1.38 g/cm3

Density of fully crystalline region(\rho_c)=1.455 g/cm3

Density of amorphous region(\rho_a)=1.335 g/cm3

Pecentage crystallinity of the sample(\chi)=?


Percentage crystallinity(\chi)=(\frac{\rho_c}{\rho} \times \frac{\rho-\rho_a}{\rho_c-\rho_a}) \times 100

By putting all given value in the formula, we get-

Percentage crystallinity(\chi)=(\frac{1.455}{1.38} \times \frac{1.38-1.335}{1.455-1.38})\times 100

Percentage crystallinity(\chi)=(\frac{1.455}{1.38} \times \frac{0.045}{0.075})\times 100

Percentage crystallinity(\chi)=(1.054 \times 0.6)\times100

Percentage crystallinity(\chi)=0.63 \times 100

Percentage crystallinity(\chi)=63 (Answer)

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