Final answer:
The change in volume, cross-sectional area, and height due to temperature changes in two blocks made of the same material is proportional to their respective initial dimensions- Block B will experience greater changes due to its larger size.
Step-by-step explanation:
Understanding the Change in Volume, Cross-Sectional Area, and Height Due to Temperature Change
When considering the effects of temperature change on materials, we need to consider thermal expansion. This process affects the volume, cross-sectional area, and height of materials, in this case, blocks A and B.
(a) For the change in volume, since the volume of Block A is 2L³, and the volume of Block B is 8L³, we expect the change in volume of B to be four times greater than that of A. This is due to the volume expansion coefficient of the material, which generally states that the change in volume is directly proportional to the initial volume.
(b) The change in the cross-sectional area would depend on the area expansion coefficient, which is similar to the volume expansion coefficient but applies to two-dimensional shapes. The initial cross-sectional area of Block A is L x 2L = 2L² and for Block B is 2L x 2L = 4L²; hence, Block B's cross-sectional area will also change more due to its larger initial area.
(c) The change in height of the blocks is also proportional to their initial heights. As Block A has an initial height of L and Block B has an initial height of 2L, the height of Block B will experience a change that is twice that of Block A's change in height, all else being equal.