GATE (TF) Textile 2021 Question Paper Solution | GATE/2021/TF/55

Question 55 (Textile Technology & Fibre Science)

Consider the following isotherms at equilibrium for two disperse dyes D₁ and D₂ dyed on polyester. If the partition coefficient of those are K₁ and K₂ respectively, the value of is __4__.

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Given in the question:

Concentration of dye D₁ in fibre(d_f)=5 g/kg
Concentration of dye D₁ in solution(d_s)=0.1 g/L

Concentration of dye D₂ in fibre(d_f)=10 g/gm
Concentration of dye D₂ in solution(d_s)=0.05 g/L

Formula:

Partition coefficient(K)=Concentration of dye in fibre(d_f)/Concentration of dye in solution(d_s)

K₁=Concentration of dye D₁ in fibre(d_f)/Concentration of dye D₁ in solution(d_s)
K₁ =5/0.1
K₁=50 L/kg

K₂=Concentration of dye D₂ in fibre(d_f)/Concentration of dye D₂ in solution(d_s)

K₂=10/0.05
K₂=200 L/kg

K₁/K₂=50/200

K2/K1=200/50
K2/K1=4 (Answer)

Solution is to written here

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