how much will the length of a 1.0 km section of concrete highway change if the temperature varies from -15 Celsius in the winter to 41 Celsius in the summer?
two 12ft sections of aluminum siding are placed end to end in the outside wall of a house.How large a gap should be atleast 2(0.09in) to keep the pices from contracting each other and buckling.
(a)
Linear coefficient of thermal expansion at 20ºC of concrete
α=12•4•10^-6 (1/ºC)
If the length at 20ºC is 1000 m, then
- at decreasing temperature the length
becomes smaller by
ΔL=L• α•ΔT=1000•12•4•10^-6•[20-(-15)]=0.42 m.
- at increasing temperature the length
becomes larger by
ΔL=L• α•ΔT=1000•12•4•10^-6•[41-20]=0.25 m.
Therefore the lenthg changes by
0.42+0.25 = 0.67 m.
(b) Temperature range ?????
To calculate the change in length of a 1.0 km section of concrete highway due to temperature variation, we need to use the coefficient of linear expansion for concrete. The coefficient of linear expansion for concrete is typically around 10 x 10^-6 per degree Celsius.
First, we calculate the temperature difference between summer and winter:
Temperature difference = Summer temperature - Winter temperature
= 41°C - (-15°C)
= 56°C
Next, we use the coefficient of linear expansion to calculate the change in length:
Change in length = Coefficient of linear expansion x Original length x Temperature difference
= (10 x 10^-6/°C) x (1.0 km) x (56°C)
Note: We need to convert 1.0 km to meters before calculations.
1.0 km = 1,000 meters
Change in length = (10 x 10^-6/°C) x (1,000 m) x (56°C)
Simplifying this equation:
Change in length = 0.00001 x 1,000 x 56 meters
= 0.56 meters
Therefore, the length of the 1.0 km section of concrete highway will change by 0.56 meters due to the temperature variation.
To determine how much the length of the concrete highway will change due to temperature variation, we need to use the coefficient of linear expansion of concrete. The linear expansion coefficient represents the amount of expansion or contraction of a material per unit length, per degree of temperature change.
Unfortunately, the coefficient of linear expansion for concrete can vary depending on its composition and other factors. However, a commonly used value for the coefficient of linear expansion for concrete is around 12 x 10^(-6) per degree Celsius.
Now, let's calculate the change in length of the 1.0 km section of concrete highway:
1. Convert the lengths to meters:
Length of the highway = 1.0 km = 1000 meters
2. Calculate the change in temperature:
ΔT (change in temperature) = Final temperature – Initial temperature
ΔT = 41°C - (-15°C) = 56°C
3. Calculate the change in length using the coefficient of linear expansion:
ΔL = L * α * ΔT
where:
ΔL = Change in length
L = Initial length of the highway
α = Coefficient of linear expansion of concrete
ΔT = Change in temperature
Plugging in the values:
ΔL = 1000 meters * (12 x 10^(-6) per °C) * 56 °C
4. Calculate the result:
ΔL = 0.00672 meters
Therefore, the length of the 1.0 km section of the concrete highway will change by approximately 0.00672 meters (or 6.72 millimeters) due to the temperature variation.