GATE (TF) Textile 2005 Question Paper Solution | GATE/2005/TF/67

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

Question 67 (Textile Engineering & Fibre Science)

If the void volume of the above sample is 0.5%, the true crystallinity of the sample is

(A)	40%
(B)	45%
(C)	50%
(D)	60%

[Show Answer]

Option B
This will be calculated by crystalline region void volume.

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

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

Density of sample( $\rho_f$ )=1.386 g/cm3

Original Volume of crystalline region( $V_c)=\frac{1}{\rho_c}$

Final volume of the crystalline region(Vc1)=Original Volume of crystalline region(Vc)-Original Volume of crystalline region x void volume %

Final volume of the crystalline region(Vc1)= $\frac{1}{1.455}-\frac{1}{1.455} \times \frac{0.5}{100}$

Final volume of the crystalline region(Vc1)=0.6838 cm3/gm

Final density of the crystalline region( $\rho_c_1)=\frac{1}{V_c1}$

Final density of the crystalline region( $\rho_c_1)=\frac{1}{0.6838}$

Final density of the crystalline region( $\rho_c_1)=1.462$ g/cm3

Crystallinity( Xcm)= $\frac{\rho_c1}{\rho_f}\times\frac{\rho_f-\rho_a}{\rho_c1-\rho_a}$

Crystallinity( Xcm)= $\frac{1.462}{1.386}\times\frac{1.386-1.335}{1.462-1.335}$

Crystallinity( Xcm)=0.43

Crystallinity( Xcm)%=0.43 x 100

Crystallinity( Xcm)%=43

Crystallinity( Xcm)%=45 (Ans)

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