Question

A steel part with surface area of 125 cm² is to be chrome coaled through an electroplating process using chromium acid sulphate as an electrolyte. An increasing current is applied to the part according to the following current time relation :

I = 12 + 0.2t

where, I = current (A) and t = time (minutes). The part is submerged in the plating solution for a duration of 20 minutes for plating purpose. Assuming the cathode efficiency of chromium to be 15% and the plating constant of chromium acid sulphate to be 2.50 × 10–2 mm³/A·s, the resulting coating thickness on the part surface is _________ μm (round off to one decimal place).

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Answer :

Correct answer is : 5.0

I = 12 + 0.2t

After time, 't', Next infinitely small time 'dt' let heat deposited 'dQ'

∴ dQ = 2.50 × 10-2 (mm3/A.s) × 12 + 0.2t × dt

As we have to convert this 's' to 'min'

∴ dQ = 2.50 × 10-2 (mm3/A × min) × 12 + 0.2t × dt

Considering cathode efficiency of 15%

dQ = 2.50 × 10-2 × 60 × (12 + 0.2t)dt × 0.15 mm3

∴ In 20 min,  Q = d Q = 0 20 2.50 × 10-2 × 60 × (12 + 0.2t)dt × 0.15

= 0.225 [ 12 + 0.1 t 2 ] 0 20 = 0.225[12 × 20 + 0.1 × 202] mm3

= 63 mm3

As area os 125 cm2

Plating thickness,  t = 63 125 × ( 100 ) = 0 .00504   m m = 5.04   μ m

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