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