Answer :

Given,

Length of the steel tape at temperature T = 27°C = 27 + 273.15 K = 300.15 K, L = 1 m

Coefficient of linear expansion of steel, α = 1.20 × 10^{-5} K^{-1}

At temperature T_{1} = 45°C = 45 + 273.15 K = 318.15 K, the length of the steel rod,

L_{1} = 63 cm = 0.63m

Let L_{2} be the actual length of the steel rod and L_{2}’ be the length measured by the steel tape at 45°C.

We know,

L_{2}’ = L + αL(T_{1} - T)

∴ L_{2}’ = 1 m + (1.20 × 10^{-5} K^{-1})(1 m)(318.15 K – 300.15 K)

⇒ L_{2}’ = 1 + 0.000216

⇒ L_{2}’ = 1.000216 m = 100.0216 cm

Hence, the actual length of the steel rod at 45°C is given by

L_{2} = (L_{2}’/L)×L_{1}

⇒ L_{2} = [(100.0216 cm)/(100 cm)](63 cm) = 63.0136 cm Therefore, the actual length of the rod at 45.0°C is 63.0136 cm. Its length at 27.0°C is 63.0 cm.

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