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Question

# Consider the following statements. (A) The coefficient of linear expansion has dimension K–1. (B) The coefficient of volume expansion has dimension K–1. (a) A and B are correct. (b) A is correct but B is wrong. (c) B is correct but A is wrong. (d) A and B are wrong.

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Solution

## (a) A and B are correct. The coefficient of linear expansion, $\alpha =\frac{1}{L}\frac{△L}{△T}\phantom{\rule{0ex}{0ex}}$ $=\frac{\left[L\right]}{\left[LT\right]}={\mathrm{K}}^{-1}$ Here, L = initial length $△$L = change in length $△$T = change in temperature On the other hand, the coefficient of volume expansion, $\gamma =\frac{1}{V}\frac{△V}{△T}=\frac{\left[{L}^{3}\right]}{\left[{L}^{3}T\right]}={\mathrm{K}}^{-1}$ Here, V = initial volume $△$V = change in volume $△$T = change in temperature K = kelvin, the S.I. unit of temperature

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