Measurement of Brass Rod Length at Different Temperatures
How does the length of a brass rod change with temperature?
When a brass rod is subjected to a change in temperature, what happens to its length?
What happens to the reading on a steel tape when measuring the length of a brass rod at different temperatures?
Does the reading on a steel tape change when measuring the length of a brass rod at varying temperatures?
Explanation:
When a brass rod is exposed to a temperature change, its length also changes due to thermal expansion. The change in length of the brass rod can be calculated using the formula ΔL brass = α brass * L 0 * ΔT, where α brass is the coefficient of linear expansion for brass, L 0 is the initial length of the brass rod, and ΔT is the change in temperature.
Similarly, the steel tape used for measuring the length of the brass rod also undergoes thermal expansion at a different rate compared to brass. The apparent length measured by the steel tape is calculated by adding the change in length of the brass rod and subtracting the change in length of the steel tape.
Detail Explanation:
Brass has a coefficient of linear expansion of 18.6 x 10⁻⁶ °C⁻¹, while steel tape has a coefficient of linear expansion of 11.7 x 10⁻⁶ °C⁻¹. When the brass rod and steel tape are both at 20.0°C, the initial reading on the steel tape for the brass rod length is 95.00 cm.
At 55.0°C, the change in length of the brass rod is approximately 0.73 cm and the change in length of the steel tape is around 0.40 cm. Therefore, the steel tape will indicate a length of approximately 95.33 cm for the brass rod at 55.0°C.
This demonstrates how thermal expansion affects the measurement of lengths and the importance of considering the coefficients of linear expansion of different materials when making precise measurements at different temperatures.