Find the dimensions of the coefficient of linear expansion α . An...

The given equation is $l_t = l_0[1 + \alpha(T_2 - T_1)]$.

Since $l_t$ and $l_0$ both represent lengths, their dimensions are $[L]$.

The quantity inside the square brackets, $1 + \alpha(T_2 - T_1)$, must be a dimensionless quantity because it is added to $1$.

Thus, the term $\alpha(T_2 - T_1)$ is dimensionless.

$[\alpha] [T_2 - T_1] = [M^0 L^0 T^0]$

Since $T_2 - T_1$ represents a change in temperature, its dimension is $[K]$.

$[\alpha] [K] = [M^0 L^0 T^0]$

$[\alpha] = [K^{-1}]$