If a 286 m steel bar is increased from 2 degrees C to 390 degrees C, how much does the bar expand?

To determine how much the steel bar expands when the temperature increases from 2 degrees Celsius to 390 degrees Celsius, one needs to apply the formula for linear thermal expansion, which is:

ΔL = L0 * α * ΔT

Where:

• ΔL is the change in length,

• L0 is the original length of the bar,

• α (alpha) is the coefficient of linear expansion for the material (for steel, this is typically around 11 x 10^-6 /°C),

• ΔT is the change in temperature in degrees Celsius.

In this scenario:

• The original length (L0) of the steel bar is 286 m.

• The change in temperature (ΔT) is 390°C - 2°C = 388°C.

• The coefficient of linear expansion (α) for steel is taken as approximately 11 x 10^-6 /°C.

Now applying the values:

ΔL = 286 m * (11 x 10^-6 /°C) * 388°C

ΔL ≈ 286 m * 0.000011 * 388

ΔL ≈ 286 m * 0.004268

ΔL ≈ 1.