A steel tape 1m long is correctly calibrated for a temperature of 27.0 °C. The length of a steel rod measured by this tape is found to be 63.0 cm on a hot day when the temperature is 45.0 °C. What is the actual length of the steel rod on that day? What is the length of the same steel rod on a day when the temperature is 27.0 °C? Coefficient of linear expansion of steel = 1.20 × 10–5 K–1
Length of the steel tape at temperature T=27oC,l=1m=100cm At temperature T1=45oC, the length of the steel rod, l1 = 63 cm Coefficient of linear expansion of steel, α=1.2×10−5 K Let l be the actual length of the steel rod and l' be the length of the steel tape at 45oC. l′−l=lα(T1−T) l′=100(1+1.20×10−5×(45−27))=100.0216cm Hence, the actual length of the steel rod measured by the steel tape at 450C can be calculated as: l2=(100.0216/100)63=63.0136cm Therefore, the actual length of the rod at 45oC is 63.0136 cm. Its length at 27oC is 63.0cm.
