Question:
Iron powder produced by gas atomization has a tap density and an apparent density of 3.26 g/cm\(^3\) and 2.66 g/cm\(^3\), respectively. The density of solid iron is 7.85 g/cm\(^3\).
Which ONE of the following options is the closest approximation to the degree of densification (in percentage) of this iron powder?
Iron powder produced by gas atomization has a tap density and an apparent density of 3.26 g/cm\(^3\) and 2.66 g/cm\(^3\), respectively. The density of solid iron is 7.85 g/cm\(^3\).
Which ONE of the following options is the closest approximation to the degree of densification (in percentage) of this iron powder?
Which ONE of the following options is the closest approximation to the degree of densification (in percentage) of this iron powder?
Show Hint
Degree of densification = tap density divided by solid density, times 100. Apparent density is not needed for this ratio.
Updated On: Aug 3, 2026
- 41.52
- 81.59
- 33.89
- 75.41
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The Correct Option is A
Solution and Explanation
Step 1: Understanding the Question:
We are given three density values for an iron powder made by gas atomization: tap density \( \rho_{tap} = 3.26\ g/cm^3 \), apparent density \( \rho_{app} = 2.66\ g/cm^3 \), and the density of solid, fully dense iron \( \rho_{s} = 7.85\ g/cm^3 \).
We need to find the degree of densification, which tells us how close the packed powder is to the fully solid metal.
Step 2: Key Formula:
Degree of densification compares the best achievable packing of the loose powder, which is the tap density after settling by vibration, with the density of the fully solid material.
\[ \text{Degree of Densification (\%)} = \frac{\rho_{tap}}{\rho_{s}} \times 100 \]
The apparent density value is extra information here, it describes how loosely the powder sits before any tapping, and is not part of this particular ratio.
Step 3: Substituting the Values:
\[ \text{Degree of Densification} = \frac{3.26}{7.85} \times 100 \]
\[ \text{Degree of Densification} = 0.41529 \times 100 = 41.53\% \]
This value is obtained by simple division and multiplication, no unit conversion is required since both densities are already in \( g/cm^3 \).
Step 4: Checking the options:
Option (A) 41.52 is essentially identical to our computed 41.53%, matching within rounding.
Option (B) 81.59 is far too high, that value is not obtained from any simple ratio of the given numbers.
Option (C) 33.89 would come from an incorrect ratio, and does not match \( \rho_{tap}/\rho_s \).
Option (D) 75.41 also does not correspond to the tap to solid density ratio.
Final Answer:
The degree of densification of the iron powder is closest to 41.52%. \[ \boxed{41.52\%} \]
We are given three density values for an iron powder made by gas atomization: tap density \( \rho_{tap} = 3.26\ g/cm^3 \), apparent density \( \rho_{app} = 2.66\ g/cm^3 \), and the density of solid, fully dense iron \( \rho_{s} = 7.85\ g/cm^3 \).
We need to find the degree of densification, which tells us how close the packed powder is to the fully solid metal.
Step 2: Key Formula:
Degree of densification compares the best achievable packing of the loose powder, which is the tap density after settling by vibration, with the density of the fully solid material.
\[ \text{Degree of Densification (\%)} = \frac{\rho_{tap}}{\rho_{s}} \times 100 \]
The apparent density value is extra information here, it describes how loosely the powder sits before any tapping, and is not part of this particular ratio.
Step 3: Substituting the Values:
\[ \text{Degree of Densification} = \frac{3.26}{7.85} \times 100 \]
\[ \text{Degree of Densification} = 0.41529 \times 100 = 41.53\% \]
This value is obtained by simple division and multiplication, no unit conversion is required since both densities are already in \( g/cm^3 \).
Step 4: Checking the options:
Option (A) 41.52 is essentially identical to our computed 41.53%, matching within rounding.
Option (B) 81.59 is far too high, that value is not obtained from any simple ratio of the given numbers.
Option (C) 33.89 would come from an incorrect ratio, and does not match \( \rho_{tap}/\rho_s \).
Option (D) 75.41 also does not correspond to the tap to solid density ratio.
Final Answer:
The degree of densification of the iron powder is closest to 41.52%. \[ \boxed{41.52\%} \]
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