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.

UCIC 202503 PHYS101 Quiz 6

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

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