The diagram below represents cross sections of equal-size beakers A, B, and C filled with beads.
Which statement best compares the porosity in the three beakers?
(1) Beaker A and beaker B have the same porosity, and beaker C has the least porosity.
(2) Beaker A and beaker B have the same porosity, and beaker C has the greatest porosity.
(3) Beaker B has the greatest porosity, beaker A has less porosity, and beaker C has the least porosity.
(4) Beaker C has the greatest porosity, beaker B has less porosity, and beaker A has the least porosity.
The Correct answer and Explanation is :
The correct answer is: (2): Beaker A and beaker B have the same porosity, and beaker C has the greatest porosity, provided C has less dense packing of beads.
To determine which statement best compares the porosity in beakers A, B, and C, we first need to clarify the concept of porosity. Porosity is defined as the ratio of the volume of voids (spaces) in a material to the total volume of the material. In the context of the beakers filled with beads, porosity refers to the amount of empty space between the beads.
Let’s consider the following points regarding the beakers:
- Visual Analysis: If we visualize the three beakers filled with beads, the arrangement and packing of the beads can significantly affect porosity. For example, if beakers A and B contain tightly packed beads with minimal gaps, their porosity will be low. In contrast, if beaker C contains beads that are loosely packed, it will have higher porosity due to the larger volume of voids between the beads.
- Comparison of Beakers:
- Beakers A and B: If the beads in both of these beakers are tightly packed with minimal space, they would have similar porosity. Therefore, the statement that they have the same porosity holds.
- Beaker C: If beaker C has beads arranged in a less dense configuration, it would have higher porosity compared to A and B.
Based on this analysis, we can make a logical comparison:
- If Beaker C is less dense, then it would have a greater porosity compared to A and B. Conversely, if A and B are densely packed, then they have lower porosity.
Conclusion
Given the possible statements:
- (1) suggests that A and B have the same porosity and that C has the least, which could be possible if C is tightly packed.
- (2) states that A and B have the same porosity while C has the greatest, which is plausible if C is loosely packed.
- (3) claims that B has the greatest porosity, which contradicts the earlier analysis unless B is the most loosely packed.
- (4) asserts that C has the greatest porosity, which aligns with the assessment if it is loosely packed compared to A and B.
Thus, the correct statement would be (2): Beaker A and beaker B have the same porosity, and beaker C has the greatest porosity, provided C has less dense packing of beads.