Coefficient of Linear Expansion and Measurement Accuracy
How does temperature affect the accuracy of measurements?
Markings to indicate length are placed on a steel tape in a room that is at a temperature of 22°C. Measurements are then made with the same tape on a day when the temperature is 27°C. Assume the objects you are measuring have a smaller coefficient of linear expansion than steel. Are the measurements (a) too long, (b) too short, or (c) accurate?
Answer:
The measurements made with the tape on a day when the temperature is 27°C will be (b) too short.
The length of material changes with temperature due to its coefficient of linear expansion. The coefficient of linear expansion of steel is 12 x 10^-6 /°C. This means that for every degree Celsius increase in temperature, the length of steel increases by 12 x 10^-6 of its original length.
In this case, the steel tape was marked at a temperature of 22°C. When the measurements are made on a day when the temperature is 27°C, the tape will have expanded due to the increase in temperature. Since the objects being measured have a smaller coefficient of linear expansion than steel, they will not have expanded as much as the tape.
Therefore, the measurements made with the tape on a day when the temperature is 27°C will be too short. This is because the tape has expanded more than the objects being measured, and therefore the measurements made with the tape will be smaller than the actual lengths of the objects.