__Question 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}.

__Solution__:*T*= 27°C,

*l*= 1 m = 100 cm

At temperature

*T*

_{1}= 45°C, the length of the steel rod,

*l*

_{1}= 63 cm

Coefficient of linear expansion of steel,

*α*= 1.20 × 10

^{–5}K

^{–1}

Let

*l*

_{2}be the actual length of the steel rod and

*l*' be the length of the steel tape at 45°C.

l' = l + αl(T

_{1}- T)

∴ l' = 100 + 1.20 X 10

^{-5}X 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:

l

_{2}= (100.0216 / 100) X 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

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