One cool 5.0 degree C spring morning, Mason lays a brick sidewalk up to his house, placing the 25 cm long bricks end to end against eachother. However, Mason forgets to leave a space for expansion and when the temperature reaches 36 degree C, the bricks buckle. How high will the bricks rise?
coefficient of expansion of brick=
10x10^-6/C^1
To find out how much the bricks will rise, we need to calculate the change in length of each brick due to the change in temperature. We can use the coefficient of expansion of the brick to do this.
The coefficient of expansion of the brick is given as 10x10^-6/C^1 (where C^1 represents the change in temperature in degrees Celsius).
First, we need to calculate the change in temperature. The temperature goes from 5.0 degrees Celsius to 36 degrees Celsius, so the change in temperature is 36 - 5.0 = 31 degrees Celsius.
Next, we can calculate the change in length using the formula:
ΔL = α × L0 × ΔT
where:
ΔL is the change in length
α is the coefficient of expansion
L0 is the initial length
ΔT is the change in temperature
Given that the initial length (L0) of each brick is 25 cm (or 0.25 meters), and the change in temperature (ΔT) is 31 degrees Celsius, we can substitute these values into the formula:
ΔL = (10x10^-6/C^1) × (0.25 meters) × (31 degrees Celsius)
Simplifying the expression, we get:
ΔL = (10 × 0.25 × 31) × 10^-6 meters
= 7.75 × 10^-4 meters
Therefore, the bricks will rise by approximately 7.75 × 10^-4 meters when the temperature increases from 5.0 degrees Celsius to 36 degrees Celsius.