A man measures the length of a steel rod by a 1 m long steel tape on a sunny day when thetemperature is 47.0 °C. The length of steel rod is found to be 60.00 cm. If the steel tape is calibratedat room temperature, what is the actual length of the rod on that day?[Use Coefficient of linear expansion of steel = 1.20 × 10–5 K-1 ]
Question
A man measures the length of a steel rod by a 1 m long steel tape on a sunny day when thetemperature is 47.0 °C. The length of steel rod is found to be 60.00 cm. If the steel tape is calibratedat room temperature, what is the actual length of the rod on that day?[Use Coefficient of linear expansion of steel = 1.20 × 10–5 K-1 ]
Solution
To find the actual length of the steel rod on the sunny day, we need to take into account the expansion of the steel tape due to the temperature difference.
First, let's calculate the change in temperature from room temperature to 47.0 °C. The change in temperature is given by:
ΔT = T2 - T1 = 47.0 °C - 20.0 °C = 27.0 °C
Next, we need to calculate the change in length of the steel tape. The change in length is given by the formula:
ΔL = α * L * ΔT
where α is the coefficient of linear expansion of steel, L is the original length of the steel tape, and ΔT is the change in temperature.
Given that the coefficient of linear expansion of steel is 1.20 × 10–5 K-1 and the original length of the steel tape is 1 m (100 cm), we can substitute these values into the formula:
ΔL = (1.20 × 10–5 K-1) * (100 cm) * (27.0 °C) = 0.0324 cm
Now, we can calculate the actual length of the rod on the sunny day by adding the change in length of the steel tape to the measured length of the rod:
Actual length = Measured length + ΔL = 60.00 cm + 0.0324 cm = 60.0324 cm
Therefore, the actual length of the rod on that sunny day is 60.0324 cm.
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