11.6. 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.
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Length of the steel tape 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 linear expansion of steel, α = 1.20 × 10–5 K–1
Let l2 be the actual length of the steel rod and l‘ be the length of the steel tape at 45°C.
l’ = l + αl(T1 – T)
∴ l’ = 100 + 1.20 × 10-5 × 100(45 – 27)
= 100.0216 cm
Hence, the actual length of the steel rod measured by the steel tape at 45°C can be calculated as:
l2 = (100.0216 / 100) × 63 = 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.
Here is your perfect answer :-
=》》》》Length of the steel tape 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 linear expansion of steel, α = 1.20 × 10–5 K–1
Let l2 be the actual length of the steel rod and l‘ be the length of the steel tape at 45°C.
l’ = l + αl(T1 – T)
∴ l’ = 100 + 1.20 × 10-5 × 100(45 – 27)
= 100.0216 cm
Hence, the actual length of the steel rod measured by the steel tape at 45°C can be calculated as:
l2 = (100.0216 / 100) × 63 = 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.