Thermal Properties of Matter
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Question : 6
Total: 22
A steel tape 1 m 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 .
Solution:
Here, length of the steel tape at 27°C is 100 cm.
∴ L = 100 c m , T = 27 ° C
The length of steel tape at 45°C isL ′ = L + Δ L
L ′ = L + α L Δ T ( ∵ Δ L = α L Δ T )
L ′ = L + α L ( T 2 – T 1 ) L ′ = 100 + ( 1.20 × 10 – 5 ) × 100 × ( 45 ° – 27 ° ) = 100.0216 c m =
Length of 63 cm measured by this tape at 45°C will be=
× 63 = 63. 0136 c m .
When temperature is 27°C, the size of 1 cm mark on the steel tape will be exactly 1 cm as the steel tape has been calibrated at 27°C.
Therefore, length of the steel of the rod at27 ° C = 63 × 1 = 63 c m
The length of steel tape at 45°C is
Length of 63 cm measured by this tape at 45°C will be
When temperature is 27°C, the size of 1 cm mark on the steel tape will be exactly 1 cm as the steel tape has been calibrated at 27°C.
Therefore, length of the steel of the rod at
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