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 .
Since the tape has been calibrated for 27 o C so on the day when temperature is 27 o C no change in division of length has been observed.
When the temperature increases to 45 o C ( Δ T = 45 − 27 = 18 o C ) , the increase observed in length of 1 cm division of the scale is,
Δ l = α l Δ T
Where α = 1.2 × 10 − 5 K -1 , l = 1 cm
Substitute the values, then
Δ l = 1.2 × 10 − 5 × 1 × 18 = 0.000216 cm
So the length of 1 cm division on tape becomes, 1 + 0.000216 = 1.000216 cm .
Since the actual length of the rod is 63 cm , therefore at day when temperature is 45 o C = 63 × 1.000216 = 63.0136 cm .
Actual length of the rod is same as 63 cm at day when temperature is 27 o C , as the division of the steel tape does not change.
Since the tape has been calibrated for
When the temperature increases to
Where
Substitute the values, then
So the length of
Since the actual length of the rod is
Actual length of the rod is same as
