GATE (TF) Textile 2018 Question Paper Solution | GATE/2018/TF/44

Question 44 (Textile Technology & Fibre Science)

If the density of 100% crystalline polyethylene is 1000 kgm^-3 and that of 100% amorphous polyethylene is 865 kgm^-3, then the mass fractional crystallinity of a polyethylene fibre with density 970 kgm^-3, accurate to two decimal places, is __0.79 to 0.81__.

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Given in the question–
Density of crystalline region( $\rho_c$ )=1000kg.m^-3

Density of amorphous region( $\rho_a$ )=865kg.m^-3

Polyethylene fibre density( $\rho$ )=970kg.m^-3

Mass fraction crystallinity of the polyethylene fibre( $\chi_c$ )=?

Formula–

$Mass fraction crystallinity(\chi_c)=\frac{\rho_c}{\rho}\times\frac{\rho-\rho_a}{\rho_c-\rho_a}$

$\chi_c=\frac{1000}{970}\times\frac{970-865}{1000-865}$

$\chi_c=\frac{1000}{970}\times\frac{105}{135}$

$\chi_c=\frac{1000\times105}{970\times135}$

$\chi_c=\frac{105000}{130950}$

$\chi_c=0.80$ (Answer)

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