Calculate the increase in length of a 250.00 meter long concrete bridge if it's temperature increases from 10.0°C to 39.0 °C? The coefficient of expansion of concrete is 9.8 X 10^-6 (1/°C)
Increase in length
= Length (m) * ΔT (° C) * coefficient of expansion (°-1)
so
In this case,
Length = 250.00 m
ΔT = 39.0 °C - 10.0 °C = 29.0 °C
coefficient of expansion = 9.8 x 10^-6 (1/°C)
Therefore, the increase in length of the concrete bridge is:
= 250.00 m * 29.0 °C * 9.8 x 10^-6 (1/°C)
= 0.0721 m or 7.21 cm (rounded to two decimal places)
Hence, the bridge would increase in length by approximately 7.21 cm if its temperature increased from 10.0°C to 39.0°C.
Why did the concrete bridge get into hot water? Because it can't handle the temperature rise!
But fear not, dear human! Let me calculate the increase in length for you. We can use the formula ΔL = L * α * ΔT, where ΔL is the change in length, L is the initial length, α is the coefficient of expansion, and ΔT is the change in temperature.
ΔL = (250.00 m) * (9.8 × 10^-6 1/°C) * (39.0 °C - 10.0 °C)
Calculating the math...
ΔL ≈ 250.00 * 9.8 × 10^-6 * 29.0
ΔL ≈ 0.072 m
So, the increase in length of the concrete bridge would be approximately 0.072 meters. Isn't it fascinating how a little change in temperature can make a big difference in length?
To calculate the increase in length of the concrete bridge, we can use the formula for linear expansion:
∆L = α * L * ∆T
Where:
∆L is the change in length
α is the coefficient of expansion
L is the original length
∆T is the change in temperature
Given:
L = 250.00 meters
α = 9.8 x 10^-6 (1/°C)
∆T = (39.0 °C) - (10.0 °C)
First, let's calculate ∆T:
∆T = 39.0 °C - 10.0 °C
∆T = 29.0 °C
Now, we can substitute the values into the formula:
∆L = (9.8 x 10^-6) * (250.00 meters) * (29.0 °C)
Calculating ∆L:
∆L = (9.8 x 10^-6) * (250.00) * (29.0)
∆L ≈ 0.0715 meters
Therefore, the increase in length of the concrete bridge is approximately 0.0715 meters (or 71.5 millimeters) when its temperature increases from 10.0°C to 39.0°C.