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 T1 = 45°C = 45 + 273.15 K = 318.15 K, the length of the steel rod,


L1 = 63 cm = 0.63m


Let L2 be the actual length of the steel rod and L2’ be the length measured by the steel tape at 45°C.


We know,


L2’ = L + αL(T1 - T)


L2’ = 1 m + (1.20 × 10-5 K-1)(1 m)(318.15 K – 300.15 K)


L2’ = 1 + 0.000216


L2’ = 1.000216 m = 100.0216 cm


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


L2 = (L2’/L)×L1


L2 = [(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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