Linear and area expansivity are properties of materials that describe how much they expand or contract when heated or cooled. Linear expansivity refers to the increase or decrease in length of a material, while area expansivity refers to the increase or decrease in the area of a material.
To solve a linear and area expansivity question, you typically need to use the following equation:
ΔL = αLΔT
ΔA = βAΔT
Where:
ΔL is the change in length of the material ΔA is the change in area of the material αL is the linear expansivity coefficient of the material βA is the area expansivity coefficient of the material ΔT is the change in temperature
Here’s an example question to help illustrate how to use these equations:
Example: A metal rod has a length of 1 meter at 20°C. If the temperature is increased to 80°C, what will be the new length of the rod? The linear expansivity coefficient of the metal is 1.2 x 10^-5 /°C.
Solution:
Using the equation ΔL = αLΔT, we can calculate the change in length of the rod:
ΔL = αLΔT ΔL = (1.2 x 10^-5 /°C) x (80°C – 20°C) ΔL = 0.00048 m
Therefore, the new length of the rod will be:
New length = 1 m + 0.00048 m = 1.00048 m
Now let’s consider an example of area expansivity:
Example: A square aluminum plate has an area of 0.5 m^2 at 25°C. If the temperature is increased to 100°C, what will be the new area of the plate? The area expansivity coefficient of aluminum is 2.3 x 10^-5 /°C.
Solution:
Using the equation ΔA = βAΔT, we can calculate the change in area of the plate:
ΔA = βAΔT ΔA = (2.3 x 10^-5 /°C) x (100°C – 25°C) ΔA = 0.0004315 m^2
Therefore, the new area of the plate will be:
New area = 0.5 m^2 + 0.0004315 m^2 = 0.5004315 m^2
These are two examples of how to solve linear and area expansivity questions using the appropriate equations.