How much will the length of a 1.0km section of concrete highway change if the temperature varies from -15 degrees Celsius in winter to 41 degrees Celsius in summer? Note: Coefficient of linear expansion for concrete is 12x10^-6.
1E5 cm * (41 - -15) * 1.2E-5 = ? cm
To find the change in length of the concrete highway section, we can use the formula:
ΔL = α * L * ΔT
where:
ΔL is the change in length,
α is the coefficient of linear expansion (given as 12x10^-6),
L is the original length of the section (given as 1.0 km), and
ΔT is the change in temperature.
First, we need to calculate the change in temperature (ΔT) by subtracting the initial temperature (-15 degrees Celsius) from the final temperature (41 degrees Celsius):
ΔT = 41°C - (-15°C)
ΔT = 41°C + 15°C
ΔT = 56°C
Now we can substitute the values into the formula:
ΔL = (12x10^-6) * (1.0 km) * (56°C)
To calculate this, we need to convert the length from kilometers to meters:
1.0 km = 1000 m
Substituting the values:
ΔL = (12x10^-6) * (1000 m) * (56°C)
Now, let's simplify the equation:
ΔL = 12 * 10^-6 * 1000 * 56 * 1°C * m°C
Since °C and m°C are both units of temperature, we can cancel them out. We're left with:
ΔL = 12 * 10^-6 * 1000 * 56 m
Calculating this:
ΔL = 0.672 m
Therefore, the length of the 1.0 km section of concrete highway will change by approximately 0.672 meters when the temperature varies from -15 degrees Celsius in winter to 41 degrees Celsius in summer.