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.

Answer 1

(a) A and B are correct.

The coefficient of linear expansion,
$\alpha =\frac{1}{L}\frac{△L}{△T}$
$=\frac{\left[L\right]}{\left[LT\right]}={\mathrm{K}}^{-1}$
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