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 formula for thermal expansion:
ΔL = L0 * α * ΔT,
where:
ΔL is the change in length,
L0 is the original length,
α is the coefficient of linear expansion,
ΔT is the 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
Setting the two equations equal to each other and solving for ΔT:
L0_steel * α_steel * ΔT = L0_brass * α_brass * ΔT
3 * 19×10^-6 * ΔT = 2.997 * 13×10^-6 * ΔT
57×10^-6 * ΔT = 38.97×10^-6 * ΔT
ΔT = 38.97 / 57 = 0.6835°C
Therefore, at a temperature of 0.6835°C, the two bars will be the same length.