Expand Your Knowledge: Linear Expansion of Brass Rod
What is the length of a brass rod when measured with a steel tape at different temperatures?
At 20.0°C, the reading is 95.00 cm. What will the tape indicate for the length of the rod when the rod and the tape are at -15.0°C?
Answer:
When the brass rod and steel tape are at -15.0°C, the steel tape will indicate a length of 94.94 cm for the brass rod.
When a student measures the length of a brass rod with a steel tape at 20.0°C and the reading is 95.00 cm, we can calculate the length of the rod at a different temperature using the formula for linear expansion:
L2 = L1[1 + α (T2 - T1)]
Where:
- L1 is the original length of the brass rod
- α is the coefficient of linear expansion of brass
- T1 is the original temperature of the brass rod and steel tape
- T2 is the new temperature of the brass rod and steel tape
- L2 is the new length of the brass rod according to the steel tape
Given values:
- L1 = 95.00 cm
- α = 18 × 10⁻⁶/°C
- T1 = 20.0°C
- T2 = -15.0°C
Substitute the values into the formula:
L2 = 95.00 cm [1 + (18 × 10⁻⁶/°C) × (-15.0°C - 20.0°C)]
L2 = 95.00 cm [1 - (18 × 10⁻⁶/°C) × 35.0°C]
L2 = 95.00 cm [1 - 0.00063]
L2 = 94.94 cm
Therefore, the steel tape will indicate a length of 94.94 cm for the brass rod when the rod and tape are at -15.0°C.