Find the dimensions of the coefficient of linear expansion . An equation involving this quantity is l_t = l₀[1 + (T₂ - T₁)] .

Step-by-step solution

The given equation is l_t = l₀[1 + (T₂ - T₁)] . Since l_t and l₀ both represent lengths, their dimensions are [L] . The quantity inside the square brackets, 1 + (T₂ - T₁) , must be a dimensionless quantity because it is added to 1 . Thus, the term (T₂ - T₁) is dimensionless. [ ] [T₂ - T₁] = [M^0 L^0 T^0] Since T₂ - T₁ represents a change in temperature, its dimension is [K] . [ ] [K] = [M^0 L^0 T^0] [ ] = [K⁻¹]