GATE (TF) Textile 2021 Question Paper Solution | GATE/2021/TF/45

Question 45 (Textile Technology & Fibre Science)

The molecular weight (M) of a polymer is determined from Mark-Houwink Equation by using coefficient K = 11.5×10−3 ml/g and exponent a = 0.73. If the measured intrinsic viscosity [η] of the solution is 6.0×102 ml/g then the value of M×10−6, (rounded off to two decimal places), is __2.70 to 3.10__.

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Formula:
\eta=KMa ,where \eta is viscosity , K is coefficient, M is molecular weight of polymer ,a is constant

As given in the question,
K=11.5×10-3 ml/g,a=0.73 and \eta=6.0×102 ml/g
By putting these values in to the formula-
\eta=KMa
6×102=11.5×10-3 xM0.73
52173.913=M0.73
M0.73=52173.913

By taking log both side-
loge(M)0.73=loge(52173.913)
0.73loge(M)=10.86,
loge(M)=14.88
M=e14.88 , (By logarithm rule, loge m n=m loge n and loge m=n to m=en)
M=2899358.3 ,
M=2.89×106
M=2.89/10-6
Mx10-6=2.89 (Answer)

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