Consider a metal rod that is 1.42 m in length at a temperature of 14.4°C. The coefficient of linear expansion is 5.22×10-5°C-1.
What is the change in length of the rod as temperature increases from 14.4°C to 52.0°C.
Change = 5.22*10^-5/oC*(52-14.4)oC = 1.96*10^-3 m. = 1.96 mm.
To calculate the change in length of the rod, we can use the formula for linear expansion:
ΔL = α * L * ΔT
Where:
ΔL is the change in length
α is the coefficient of linear expansion
L is the original length of the rod
ΔT is the change in temperature
Given:
L = 1.42 m (original length)
α = 5.22×10^(-5) °C^(-1) (coefficient of linear expansion)
ΔT = 52.0°C - 14.4°C = 37.6°C (change in temperature)
Substituting the values into the formula:
ΔL = (5.22×10^(-5) °C^(-1)) * (1.42 m) * (37.6°C)
Now let's calculate the change in length:
ΔL = (5.22×10^(-5) °C^(-1)) * (1.42 m) * (37.6°C)
= 0.027767 m
Therefore, the change in length of the rod as the temperature increases from 14.4°C to 52.0°C is approximately 0.0278 meters (or 27.8 millimeters).