Temperature and Measurement: Understanding Thermal Expansion

How does temperature affect measurements?

Can you calculate the correct distance given a measurement taken at a different temperature?

Understanding Thermal Expansion and Correct Measurement Calculation

Temperature plays a crucial role in affecting measurements, especially when dealing with materials that expand or contract with temperature changes. In this case, a 100' steel tape was used to measure a distance of 10,000.00' at a temperature of 98 degrees Fahrenheit. To calculate the correct distance considering the initial measurement at a different temperature, we need to understand the concept of thermal expansion.

The formula for linear thermal expansion is:

ΔL = α x L₀ x ΔT

Where:

ΔL is the change in length

α is the coefficient of linear expansion for the material

L₀ is the original length at the initial temperature

ΔT is the change in temperature

Given the coefficient of linear expansion for steel as approximately 0.0000065 per degree Fahrenheit, we can calculate the correct distance as follows:

Original length (L₀) = 100 feet

Initial temperature (T₀) = 68 degrees Fahrenheit

Final temperature (T) = 98 degrees Fahrenheit

Change in temperature (ΔT) = T - T₀ = 98°F - 68°F = 30°F

By applying the formula, we can determine the change in length (ΔL) of the steel tape due to the temperature change, which in this case is a positive value indicating expansion. Subtracting this change from the original length gives us the correct distance:

Correct Distance = 100 feet - 0.0195 feet

Correct Distance = 99.9805 feet

Therefore, the correct distance when the tape was manufactured at a temperature of 68 degrees Fahrenheit is approximately 99.9805 feet.