How does temperature affect the measurement of length?

Question:

What happens to the length of an aluminum rod measured with a steel tape at 25°C when both the rod and tape are at 0°C?

Answer:

The tape will indicate a different length for the rod when both the tape and the rod are at 0°C due to the thermal expansion of the materials.

When measuring the length of an object, the effects of thermal expansion must be taken into consideration. Different materials expand or contract at different rates when subjected to temperature changes. This phenomenon is known as thermal expansion.

In the case of an aluminum rod measured with a steel tape, both materials have different coefficients of linear expansion. This means they expand or contract at different rates when heated or cooled.

To calculate the length of the rod at a different temperature, we need to consider the thermal expansion of both the rod and the tape. The formula to calculate the change in length due to thermal expansion is ΔL = α * L * ΔT, where ΔL is the change in length, α is the coefficient of linear expansion, L is the original length, and ΔT is the change in temperature.

By calculating the change in length for both the rod and the tape using their respective coefficients of linear expansion, we can determine the length indicated by the tape at the desired temperature. This highlights the importance of understanding thermal expansion in the measurement of length.