Which of the following is the correct set of formula for thermal expansion in solid objects?

Question

BlackTom AI · Accepted Answer

To tackle this question, I will compare each option against the standard formulas for thermal expansion in solids.
Option a: ΔL = α Li ΔT, ΔA = 3α Ai ΔT, ΔV = 2α Vi ΔT.
- The correct linear expansion term is ΔL = α L ΔT, so ΔL here is fine if L is Li, but the area and volume terms are swapped incorrectly: ΔA should be 2αAΔT, not 3αAΔT, and ΔV should be 3αVΔT, not 2αVΔT. This makes option a incorrect overall.
Option b: ΔL = 2α Li ΔT, ΔA = α Ai ΔT, ΔV = 3α Vi ΔT.
- The linear term is wrong: it should be ΔL = αLiΔT, not 2α. The area term would require a factor of 2, not 1, so ΔA = αAiΔT is incorrect. The volume term 3αViΔT is correct, but since two terms are wrong, option b is incorrect.
Option c: ΔL = α Li ΔT, ΔA = 2α Ai ΔT, ΔV = 3α Vi ΔT.
- Here the linear expansion matches the standard form ΔL = αLΔT with L = Li. The area expansion factor is 2α, which is correct for ΔA = 2αAΔT, where A = Ai. The volume expansion uses 3α, yielding ΔV = 3αVΔT with V = Vi. All three parts align with the correct general relationships, so option c is internally consistent and correct.
Option d: ΔL = 3α Li ΔT, ΔA = 2α Ai ΔT, ΔV = α Vi ΔT.
- This option incorrectly assigns the coefficients: linear term should be α, not 3α; area term is correct with 2α, but the volume term should be 3αViΔT, not αViΔT. The mismatched coefficients reveal fundamental errors in the expansion relations, making option d incorrect.
In summary, the only set of formulas that consistently uses the standard coefficients—ΔL = αLΔT, ΔA = 2αAΔT, and ΔV = 3αVΔT—is option c. The other options misstate one or more coefficients, leading to incorrect expressions for at least one of the dimensions.

Which of the following is the correct set of formula for thermal expansion in solid objects?单项选择题

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