GATE (TF) Textile 2005 Question Paper Solution | GATE/2005/TF/66

The apparent crystallinity of a PET sample by density method is found to be 45%. The density of amorphous and crystalline PET sample is 1.355 and 1.455 g/cm³ respectively.

Question 66 (Textile Engineering & Fibre Science)

The density of the sample in g/cm³ will be

(A)	1.335
(B)	1.366
(C)	1.386
(D)	1.455

[Show Answer]

Option C
CRYSTALLINITY %=45

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

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

Density of sample( $\rho_f$ )=?

By formula-

Crystallinity( Xcm)= $\frac{\rho_c}{\rho_f}\times\frac{\rho_f-\rho_a}{\rho_c-\rho_a}$

0.45= $\frac{1.455}{\rho_f}\times\frac{\rho_f-1.335}{1.455-1.335}$

0.45= $\frac{1.455}{\rho_f}\times\frac{\rho_f-1.335}{0.12}$

$0.45 \times 0.12 \times \rho_f=1.455 \times (\rho_f-1.335)$

$0.054 \times \rho_f =1.455 \times \rho_f-1.942$

$1.942=1.455 \times \rho_f-0.054 \times \rho_f$

$1.942=1.401 \times \rho_f$

$\rho_f=\frac{1.942}{1.401}$

$\rho_f=1.386$ (Ans)

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