Linear Expansion Calculation: Steel Tape Length at Different Temperatures

What is the initial length of the steel tape and how does temperature affect it?

The steel tape measures 200.00 m at 15⁰C. What will be its length at 55⁰C?

Answer:

The length of the steel tape at 55 degrees Celsius is 200.096 meters, calculated using the linear expansion formula.

Linear expansion is a phenomenon where an object expands or contracts in response to changes in temperature. In the case of the steel tape, its original length at 15⁰C is 200.00 meters.

As the temperature increases to 55⁰C, the steel tape will expand due to the heat. The coefficient of linear expansion for steel is typically 0.000012/C°, which means that for every degree Celsius increase in temperature, the steel tape will expand by 0.000012 times its original length.

By applying the formula for linear expansion, ΔL = L0 * α * ΔT, where ΔL is the change in length, L0 is the original length, α is thecoefficient of linear expansion, and ΔT is the change in temperature, we can calculate the change in length of the steel tape.

In this case, the change in temperature is 40°C (55°C - 15°C). By substituting the values into the formula, we can determine that the steel tape will increase in length by 0.096 meters or 96 millimeters when the temperature rises to 55⁰C.

Therefore, the final length of the steel tape at 55°C will be its original length of 200.00 meters plus the change in length, resulting in a total length of 200.096 meters.

Understanding how temperature affects the length of materials like steel can be crucial in various fields such as engineering, construction, and manufacturing. By knowing the properties of materials and how they respond to temperature changes, professionals can make informed decisions and prevent potential issues in their projects.