Find the true total distance chained:

A chain was calibrated to be of exact length 30.00 m at 20^oC. When this chain was used for chain surveying within field, the temperature was recorded to be 45^oC. If the coefficient of linear expansion of steel used in chain is 8 × 10^{- 6} per ^oC, find the true total distance chained if measured distance on ground is 6000 m.

Solution

True length of chain at 20^oC = 30.00 m

True length of chain at 45^oC would be L = L₀ (1 + α t)

= 30.00 [1 + (8 × 10^-6) × (45 - 20)]

= 30.00 × (1 + 0.0002) = 30.06 m

True measure distance 30.06/30.00× 6000 = 6012 m.