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Are searcher conducts electrochemical machining (ECM) on a binary alloy (density 6000 kg/m3) of iron (atomic weight 56, valency 2) and metal P (atomic weight 24, valency 4). Faraday's constant = 96500 coulomb/mole. Volumetric material removal rate of the alloy is 50 mm3/s at a current of 2000 A. The percentage of the metal P in the alloy is closest to
[2008]
  • a)
    40
  • b)
    25
  • c)
    15
  • d)
    79
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
Are searcher conducts electrochemical machining (ECM) on a binary allo...
Given data:
p= 6000kg/m3=6gm/cr
MRR(Q)=50mm3/s
50x10-3 CC/S

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Most Upvoted Answer
Are searcher conducts electrochemical machining (ECM) on a binary allo...
Given:
- Density of the binary alloy = 6000 kg/m3
- Atomic weight of iron (Fe) = 56
- Valency of iron = 2
- Atomic weight of metal P = 24
- Valency of metal P = 4
- Faraday's constant = 96500 C/mol
- Volumetric material removal rate = 50 mm3/s
- Current = 2000 A

To find:
The percentage of metal P in the alloy.

Solution:
The volumetric material removal rate (MRR) can be calculated using the formula:

MRR = (I * K * Q) / (ρ * A)

Where:
- I is the current in amperes (A)
- K is the electrochemical machining constant
- Q is the electrochemical equivalent of the material in mol/C
- ρ is the density of the material in kg/m3
- A is the atomic weight of the material in g/mol

Step 1: Calculate the atomic weight of the alloy.

The atomic weight of the alloy (Aalloy) can be calculated as the weighted average of the atomic weights of iron (AFe) and metal P (AP) based on their percentage composition:

Aalloy = (AP * %P + AFe * �) / 100

Since the alloy is a binary alloy, %P + � = 100.

Step 2: Calculate the electrochemical equivalent of the alloy.

The electrochemical equivalent of the alloy (Qalloy) can be calculated using the formula:

Qalloy = (QFe * � + QP * %P) / 100

Where:
- QFe is the electrochemical equivalent of iron in mol/C
- QP is the electrochemical equivalent of metal P in mol/C

Step 3: Calculate the percentage of metal P in the alloy.

The percentage of metal P in the alloy (%P) can be calculated using the formula:

%P = (Qalloy * 100) / (QP * Aalloy)

Substituting the values into the formulas:

- AFe = 56
- AP = 24
- � = 100 - %P
- QFe = (Faraday's constant) / (Valency of Fe)
- QP = (Faraday's constant) / (Valency of P)

Step 4: Substitute the given values and calculate the percentage of metal P.

Using the given values:
- Density of the alloy (ρ) = 6000 kg/m3
- Current (I) = 2000 A
- Volumetric material removal rate (MRR) = 50 mm3/s

Convert the MRR from mm3/s to m3/s:
MRR = 50 * 10^-9 m3/s

Substitute the values into the formula for MRR:

MRR = (I * K * Qalloy) / (ρ * Aalloy)

Solve the equation for Qalloy:

Qalloy = (MRR * ρ * Aalloy) / (I * K)

Substitute the calculated values of Aalloy and Qalloy into the formula for %P:

%P = (Qal
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Are searcher conducts electrochemical machining (ECM) on a binary alloy (density 6000 kg/m3) of iron (atomic weight 56, valency 2) and metal P (atomic weight 24, valency 4). Faradays constant = 96500 coulomb/mole. Volumetric material removal rate of the alloy is 50 mm3/s at a current of 2000 A. The percentage of the metal P in the alloy is closest to[2008]a)40b)25c)15d)79Correct answer is option 'B'. Can you explain this answer?
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