Assertion (A): The coefficient of volume expansion of a solid is approximately three times its coefficient of linear expansion. Reason (R): Volume is a three-dimensional property derived from cubing the linear dimension.
A.Both A and R are true but R is NOT the correct explanation of A.
B.A is true but R is false.
C.A is false but R is true.
D.Both A and R are true and R is the correct explanation of A.
Explanation:
The coefficient of linear expansion is alpha. A cube of side L has volume V = L^3. When heated, the new length is L(1+alphadT). The new volume is [L(1+alphadT)]^3. Expanding via binomial theorem and ignoring higher-order small terms gives V' = V(1 + 3alphadT). Thus, the volume expansion coefficient gamma is equal to 3alpha. Reason R correctly explains Assertion A.
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