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

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

• A. 9.88 m
• B. 1.33 m
• C. 2.93 m
• D. 7.23 m

Answer: (B)

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.

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.