SAT Subject Physics Practice Question 298: Answer and Explanation

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Question: 298

69. Which of the following equations best states the relationship between a material’s coefficient of volume expansion due to heating, β, and its coefficient of linear expansion, α?

A. β = α
B. β = 3α
C. β = α + α2
D. β = α3
E. β = 3α3

Correct Answer: B

Explanation:

Since the coefficient of thermal expansion has units of deg−1 whether it’s for linear, area, or volume expansion, we can eliminate C, D, and E, because the units of β would be wrong if any of these equations were true. Now, all you need to remember is that the coefficient of volume expansion is different from the coefficient of linear expansion to eliminate A and choose B. [In case you want to see how B is derived, notice that since each linear dimension, L, of a solid increases by αLΔT, the new volume of a heated solid, V′, is V(1 + αΔT)3 = V(1 + 3αΔT + 3α2ΔT + α3ΔT). Since α is so small, the terms involving α2 and α3 are really small and can be i

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