The New River Gorge bridge in West Virginia is a 514 m long steel arch. How much will its length change between temperature extremes -20.3 degrees C and 32.7 degrees C
Linear expansion coefficient α=ΔL/L•ΔT
For steel α =12•10⁻⁶ (1/℃)
ΔL=α• L •ΔT=
=12•10⁻⁶•514•(32.7+20.3)=0.327 m
To calculate the change in length of the New River Gorge bridge between temperature extremes, we can use the coefficient of linear expansion (α) of the material. The coefficient of linear expansion represents how much a material expands or contracts per unit length for each degree Celsius change in temperature.
The formula to calculate the change in length (ΔL) is:
ΔL = α * L0 * ΔT
Where:
- ΔL is the change in length
- α is the coefficient of linear expansion
- L0 is the initial length of the bridge
- ΔT is the change in temperature
For steel, the coefficient of linear expansion is approximately 12 * 10^(-6) per degree Celsius. Therefore, we need to convert the temperature difference from Celsius to Kelvin by adding 273.15 to the values.
Let's calculate it step by step:
1. Convert the given temperatures into Kelvin:
-20.3 °C + 273.15 = 252.85 K (temperature in Kelvin)
32.7 °C + 273.15 = 305.85 K (temperature in Kelvin)
2. Calculate the change in temperature:
ΔT = T2 - T1 = 305.85 K - 252.85 K = 53 K
3. Substitute the values into the formula:
ΔL = α * L0 * ΔT = (12 * 10^(-6) / °C) * 514 m * 53 K
= (12 * 10^(-6)) * 514 m * 53
4. Calculate the change in length:
ΔL = 0.000012 * 514 * 53 m
= 0.00038304 m
Therefore, the length change of the New River Gorge bridge between temperature extremes of -20.3 °C and 32.7 °C is approximately 0.00038304 meters.