Quick check from College Physics, 13.2 Thermal Expansion of Solids and Liquids

Thermal Expansion of Solids and Liquids: quick check

Two blocks, A and B, are made of the same material. Block A has dimensions $l \times w \times h = L \times 2 L \times L$ and Block B has dimensions $2 L \times 2 L \times 2 L$ . If the temperature changes, what is (a) the change in the volume of the two blocks, (b) the change in the cross-sectional area $l \times w$ , and (c) the change in the height $h$ of the two blocks?

There are two rectangular blocks. Block A has its dimensions labeled length equals L, width equals two times L, height equals L. Block B has its dimensions labeled length, width, and height all equal to two times L.

Figure 13.15

Answer it in your own words before you look.

Answer
(a) The change in volume is proportional to the original volume. Block A has a volume of $L \times 2 L \times L = {2 L}^{3} .$ ^. Block B has a volume of $2 L \times 2 L \times 2 L = {8 L}^{3},$ which is 4 times that of Block A. Thus the change in volume of Block B should be 4 times the change in volume of Block A.
(b) The change in area is proportional to the area. The cross-sectional area of Block A is $L \times 2 L = {2 L}^{2},$ while that of Block B is $2 L \times 2 L = {4 L}^{2} .$ Because cross-sectional area of Block B is twice that of Block A, the change in the cross-sectional area of Block B is twice that of Block A.
(c) The change in height is proportional to the original height. Because the original height of Block B is twice that of A, the change in the height of Block B is twice that of Block A.

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