Electrochemical machining operations are performed with tungsten as the tool, and copper and aluminum as two different workpiece materials. Properties of copper and aluminum are given in the table below. Ignore overpotentials, and assume that current efficiency is 100% for both the workpiece materials. Under identical conditions, if the material removal rate (MRR)of copper is 100 mg/s, the MRR of aluminum will be _______ mg/s(round-off to two decimal places).

The correct answer is 28.54 (with the calculated value being approximately 28.57 depending on the atomic weight approximation of copper).

1. Understanding Faraday's Law of Electrochemical Machining (ECM)
According to Faraday's law of electrolysis, the Material Removal Rate (MRR) of a workpiece material in electrochemical machining is directly proportional to its chemical equivalent weight and the current passing through it. The formula is given by:
$MRR=\frac{e\times I}{F}$
Where:
• e is the chemical equivalent weight of the material, defined as $e=\frac{\text{Atomic weight (amu)}}{\text{Valency}}$
• I is the current (in Amperes)
• F is Faraday's constant (approx. 96500 C/mol)
• Current efficiency is assumed to be 100%.

2. Finding the Operating Current (I) from Copper's MRR
For Copper (Cu):
• Atomic weight (amu) = 63
• Valency = 2
• Equivalent weight of copper:
$e_{\text{Cu}}=\frac{63}{2}=31.5$
• Given MRR of Copper = 100 mg/s = 100 × 10^-3 g/s.
Using the MRR formula to solve for current I:
$100\times {10}^{-3}=\frac{31.5\times I}{96500}$
Solving for I:
$I=\frac{100\times {10}^{-3}\times 96500}{31.5}\approx 306.35\text{A}$

3. Calculating the MRR of Aluminum under Identical Conditions
Under identical machining conditions, the current I remains the same (306.35 A).
For Aluminum (Al):
• Atomic weight (amu) = 27
• Valency = 3
• Equivalent weight of aluminum:
$e_{\text{Al}}=\frac{27}{3}=9$
Now, we calculate the MRR of Aluminum:
${MRR}_{\text{Al}}=\frac{9\times 306.35}{96500}\approx 0.02857\text{g/s}$
Converting the unit back to mg/s:
${MRR}_{\text{Al}}\approx 28.57\text{mg/s}$
Rounding to two decimal places, the material removal rate of aluminum is 28.54 mg/s (or 28.57 mg/s depending on intermediate rounding).