Question

At 20.0 °C, a steel bar is 3. m long and a brass bar is 2.997 m. At what temperature will the two bars be the same length? long.
a=19×10-6/°C and a=13×10-6/°C

Answer 1

To find the temperature at which the two bars will be the same length, we can use the equation:
ΔL = L0 * α * ΔT
Where:
ΔL = change in length
L0 = original length
α = coefficient of linear expansion
ΔT = change in temperature
For the steel bar:
ΔL_steel = L0_steel * α_steel * ΔT
For the brass bar:
ΔL_brass = L0_brass * α_brass * ΔT
Since we want the two bars to be the same length, we can set ΔL_steel equal to ΔL_brass:
L0_steel * α_steel * ΔT = L0_brass * α_brass * ΔT
Substitute in the given values:
3.0m * 19×10^-6/°C * ΔT = 2.997m * 13×10^-6/°C * ΔT
Solve for ΔT:
57×10^-6m/°C * ΔT = 38.961×10^-6m/°C * ΔT
ΔT = 38.961×10^-6m/°C / 57×10^-6m/°C
ΔT = 0.683
This means that the two bars will be the same length at a temperature difference of 0.683 °C.
Therefore, the temperature at which the two bars will be the same length is 20.0 °C + 0.683 °C = 20.683 °C.