A steel tape 1m long Is correctly calibrated for a temperature of 27.0

1.	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» 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

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»

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