Question

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^-5K^-1.

Answer 1

l₀ = 63 cm 

∆T = 45°C – 27°C . 

= 18°C = 18 K 

α = 1.2 × 10^-5K^-1 

l = l₀ (1 + α ∆T) 

= 63(1 + 1.2 × 10^-5 × 18) 

l = 63.0136 cm.

∴ Actual length of the steel rod at 45°C = 63.0136 cm 

At 27°C, the steel tape is correctly calibrated. 

∴ the length of the steel rod = 63.0 cm