# 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 + α^{2}

D. β = α^{3}

E. β = 3α^{3}

**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 α*L*Δ*T*, the new volume of a heated solid, *V*′, is *V*(1 + αΔ*T*)^{3} = *V*(1 + 3αΔ*T* + 3α^{2}Δ*T* + α^{3}Δ*T*). Since α is so small, the terms involving α^{2} and α^{3} are *really* small and can be i