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( $\chi$ )=?

Formula:

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

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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