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The length of copper rod at 50°c is 2.0016m and at 200°c is 2.00664. Find the length at 0°c and the linear expansivity of the copper?
andersonvictory
11 Jan, 2024
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ΔΘ = 200 - 50 = 150 °C
ΔL = 2.00664 – 2.00166 = 0.00498 m
Linear Expansivity, α = ΔL/LΔΘ
=> α = 0.00498/(2.00166 × 150)
=> α = 1.6586 × 10‐⁵ °C‐¹p
Calculating L at 0°C
ΔΘ = 0 - 50 = -50 °C
Taking L1 = 2.00166 m as our initial length at 50 °C
Taking L2 as the second length at 0°C
So, L2 = L1 + ΔL
Calculating ΔL
From Linear Expansivity equation
ΔL = αL1ΔΘ = 1.6586 × 10‐⁵ × 2.00166 × -50
ΔL = -0.00166
=> L2 = 2.00166 + (-0.00166)
=> L2 = 2.00166 - 0.00166 = 2.00m
Therefore, the length of the copper at 0°C is 2.00m
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