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.

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