1. A brass rod is 2m long at a certain temperature. What is itslength for a temperature rise of 100k if the expansivity ofbrass is 1.8 x ?2. The linear expansivity of a material of a cube is 1.2 x10 -6 K -1 .If the length of each side of the cube is 10cm, find the areaof one face of the cube and the volume of the cube whenits temperature is raised by 30k.
Question
- A brass rod is 2m long at a certain temperature. What is itslength for a temperature rise of 100k if the expansivity ofbrass is 1.8 x ?2. The linear expansivity of a material of a cube is 1.2 x10 -6 K -1 .If the length of each side of the cube is 10cm, find the areaof one face of the cube and the volume of the cube whenits temperature is raised by 30k.
Solution
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The change in length of a material due to temperature change can be calculated using the formula:
ΔL = α * L0 * ΔT
where: ΔL is the change in length, α is the coefficient of linear expansion (also known as expansivity), L0 is the original length, and ΔT is the change in temperature.
In this case, α = 1.8 x 10^-5 K^-1, L0 = 2m, and ΔT = 100K. Substituting these values into the formula gives:
ΔL = 1.8 x 10^-5 K^-1 * 2m * 100K = 0.036m
Therefore, the length of the brass rod after a temperature rise of 100K is 2m + 0.036m = 2.036m.
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The change in length of each side of the cube due to temperature change can be calculated using the same formula as above. In this case, α = 1.2 x 10^-6 K^-1, L0 = 10cm = 0.1m, and ΔT = 30K. Substituting these values into the formula gives:
ΔL = 1.2 x 10^-6 K^-1 * 0.1m * 30K = 0.0000036m = 0.0036cm
Therefore, the length of each side of the cube after a temperature rise of 30K is 10cm + 0.0036cm = 10.0036cm.
The area of one face of the cube is given by the formula A = L^2, where L is the length of a side. Substituting L = 10.0036cm into this formula gives:
A = (10.0036cm)^2 = 100.07201296cm^2
The volume of the cube is given by the formula V = L^3. Substituting L = 10.0036cm into this formula gives:
V = (10.0036cm)^3 = 1001.108717577216cm^3.
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