Asteel 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 tobe 63.0 cm on a hot day when the temperature is 45.0 °C. What isthe actual length of the steel rod on that day? What is the length ofthe same steel rod on a day when the temperature is 27.0 °C? Coefficient of linear expansion of steel = 1.20 × 10–5K–1.
Asteel 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 tobe 63.0 cm on a hot day when the temperature is 45.0 °C. What isthe actual length of the steel rod on that day? What is the length ofthe same steel rod on a day when the temperature is 27.0 °C? Coefficient of linear expansion of steel = 1.20 × 10–5K–1.
Length of the steeltape at temperature T = 27°C, l = 1 m = 100 cm
At temperature T1= 45°C, the length of the steel rod, l1 = 63 cm
Coefficient of linearexpansion of steel, α= 1.20 × 10–5 K–1
Let l2be the actual length of the steel rod and l' be the length ofthe steel tape at 45°C.
Hence, the actuallength of the steel rod measured by the steel tape at 45°C can becalculated as:
= 63.0136 cm
Therefore, the actuallength of the rod at 45.0°C is 63.0136 cm. Its length at 27.0°Cis 63.0 cm.
Length of the steeltape at temperature T = 27°C, l = 1 m = 100 cm
At temperature T1= 45°C, the length of the steel rod, l1 = 63 cm
Coefficient of linearexpansion of steel, α= 1.20 × 10–5 K–1
Let l2be the actual length of the steel rod and l' be the length ofthe steel tape at 45°C.
Hence, the actuallength of the steel rod measured by the steel tape at 45°C can becalculated as:
= 63.0136 cm
Therefore, the actuallength of the rod at 45.0°C is 63.0136 cm. Its length at 27.0°Cis 63.0 cm.
