GATE (TF) Textile 2007 Question Paper Solution | GATE/2007/TF/76

Given the length of crystalline region as 90 $\mathring{A}$ , crystalline density of polyester as 1.445 g/cc and amorphous density as 1.335 g/cc.

If the density of polyester fibres is 1.399 g/cc, the fractional density crystallinity of polyester would be approximately

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Option C is correct.
Given-
Length of crystalline region(Lc)= $90 A^o$

Crystalline density( $\rho_c$ )=1.445 g/cc

Amorphous density( $\rho_a$ )=1.335 g/cc

Density of fibre( $\rho$ )=1.399 g/cc

Fractional crystallinity=?

Formula-

Fractional crystallinity= $\frac{\rho_c}{\rho} \times \frac{\rho-\rho_a}{\rho_c-\rho_a}$

Fractional crystallinity= $\frac{1.445}{1.399} \times \frac{1.399-1.335}{1.445-1.335}$

Fractional crystallinity= $1.033 \times \frac{0.064}{0.11}$

Fractional crystallinity= $1.033 \times 0.58$

Fractional crystallinity=0.60 (Ans)