Final answer:
The volume, cross-sectional area, and height changes due to temperature changes are proportional to the original size measurements of Blocks A and B. Block B, having larger dimensions (2L x 2L x 2L), will experience a greater change in all aspects compared to Block A (L x 2L x L) when subject to the same temperature change.
Step-by-step explanation:
When considering the effects of a temperature change on two blocks, A and B, with different dimensions, we need to understand how their physical properties will adjust accordingly. Block A has dimensions L x 2L x L, while Block B is larger with dimensions 2L x 2L x 2L. Both blocks are made of the same material, so their expansion properties due to temperature changes will be similar.
Volume Change
(a) Since volume is a cubic measurement, a small change in temperature will result in a change in volume that is proportional to each block's original volume. For Block A, the volume is L x 2L x L, whereas for Block B, it is 2L x 2L x 2L. Thus, Block B will experience a greater change in volume as it has a larger original volume.
Cross-sectional Area Change
(b) The cross-sectional area (l x w) is affected by temperature changes, and since the area is proportional to the size of each side, any change will also be proportional. Block A's cross-sectional area is calculated as L x 2L, which is 2L², while Block B has a cross-sectional area of 2L x 2L or 4L². As Block B's cross-sectional area is twice that of Block A's, any change will similarly be twice as great for Block B compared to Block A.
Height Change
(c) Lastly, the change in height (h) due to temperature change will be proportional to the original height. Block B has twice the original height of Block A. Therefore, the change in height for Block B will be twice that of Block A.