Which equation correctly represents linear thermal expansion for a change in length ΔL?

Which equation correctly represents linear thermal expansion for a change in length ΔL?

• A. ΔL = α ΔT
• B. ΔL = α ΔT / L
• C. ΔL = α L ΔT
• D. ΔL = α L^2 ΔT

Answer: (A)

Linear thermal expansion shows that how much a material’s length changes depends on both the temperature change and the original length. The coefficient α gives how much length changes per degree per unit length, so the change scales with L. The correct form is ΔL = α L ΔT because the fractional change in length is ΔL/L = α ΔT. This ensures longer objects expand more in absolute length under the same temperature rise, and the units make sense: α has units of 1/°C, so α ΔT is dimensionless, and multiplying by L gives a length. If you tried ΔL = α ΔT, you’d predict the same absolute expansion for rods of any original length, which isn’t observed. The proportional form ΔL/L = α ΔT is just another way to express the same relationship.

Linear thermal expansion shows that how much a material’s length changes depends on both the temperature change and the original length. The coefficient α gives how much length changes per degree per unit length, so the change scales with L. The correct form is ΔL = α L ΔT because the fractional change in length is ΔL/L = α ΔT. This ensures longer objects expand more in absolute length under the same temperature rise, and the units make sense: α has units of 1/°C, so α ΔT is dimensionless, and multiplying by L gives a length.

If you tried ΔL = α ΔT, you’d predict the same absolute expansion for rods of any original length, which isn’t observed. The proportional form ΔL/L = α ΔT is just another way to express the same relationship.