A brass lid screws tightly onto a glass jar at 20 oC. To help open the jar, it can be placed into a bath of hot water. After this treatment, the temperature of the lid and the jar are both 60 oC. The inside diameter of the lid is 8.0 cm at 20 oC. Find the size of the gap (difference in radius) that develops by this procedure.
so radius - 4.0cm
is this the right equation for it?
delta L = alpha (initial Length) (delta Temp)
Dear Bobpursely
You're a terribly teacher.
No. You need to work with area expansion, find the new diameter from area, then the change in area.
:O our teacher never mentioned area expansion..
Yes, the equation you mentioned is the correct equation to use in this scenario. It is known as the thermal expansion equation, which is applicable to linear expansion. In this case, since we are dealing with the gap between the lid and the jar, we need to use the equation for radial or linear expansion.
However, in this particular problem, we are given the temperature change and the initial diameter of the lid instead of the initial length. Therefore, we should modify the equation slightly to account for the radial expansion:
ΔL = α * (initial Diameter) * ΔT
Where:
ΔL is the change in length (or radius in this case)
α is the coefficient of linear expansion
(initial Diameter) is the initial diameter of the lid
ΔT is the change in temperature
Since we are looking for the size of the gap (difference in radius), we can divide the change in length by 2, as the radius is half the diameter. So the equation becomes:
ΔR = α * (initial Diameter) * ΔT / 2
Now we can plug in the values given in the problem:
α (coefficient of linear expansion for brass) = 19 × 10^-6 / oC
(initial Diameter) = 8.0 cm
ΔT = (60 - 20) oC = 40 oC
ΔR = (19 × 10^-6 / oC) * (8.0 cm) * (40 oC) / 2
Calculating this expression will give you the size of the gap (difference in radius) that develops after the treatment.