A railroad track made of steel has a length of 55 m when the temperature is 0°C. What is its length

Source: JAMB · 2023

A railroad track made of steel has a length of 55 m when the temperature is 0°C. What is its length on a hot day when the temperature is 40.0°C? [α = 1.1 x 10-5 (°C)-1]

A railroad track made of steel has a length of 55 m when the temperature is 0°C. What is its length on a hot day when the temperature is 40.0°C? [α = 1.1 x 10-5 (°C)-1]

  1. 55.0242 m ✓
  2. 55.0422 m
  3. 55.242 m
  4. 55.422 m
Explanation

Step 1: Identify given values and what to find
Given: L₀ = 55 m, T₁ = 0°C, T₂ = 40°C, α = 1.1 × 10⁻⁵ °C⁻¹
Find: Final length L

Step 2: Calculate temperature change
ΔT = T₂ – T₁ = 40 – 0 = 40°C

Step 3: Write linear expansion formula
Formula: L = L₀(1 + αΔT)

Step 4: Substitute and calculate
L = 55(1 + 1.1 × 10⁻⁵ × 40)
L = 55(1 + 4.4 × 10⁻⁴)
L = 55(1.00044)
L = 55.0242 m

Step 5: The answer is 55.0242 m

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