The Stanford linear accelerator contains hundreds of brass disks tightly fitted into a steel tube (see figure). The coefficient of linear expansion of the brass is 2.00 *10^-5 per C$\degree$. The system was assembled by cooling the disks in dry ice (-57$\degree$C) to enable them to just slide into the close-fitting tube. If the diameter of a disk is 80.00 mm at 43$\degree$C, what is its diameter in the dry ice?

Question

Quizplus · Accepted Answer

We can use the formula:
ΔL = αLΔT
where ΔL is the change in length, α is the coefficient of linear expansion, L is the original length, and ΔT is the change in temperature.

In this case, we want to find the change in diameter, which is twice the change in length:
ΔD = 2ΔL

We know that the initial diameter (at 43°C) is 80.00 mm, so the initial radius is 40.00 mm.

The temperature change is:
ΔT = -57°C - 43°C = -100°C

We can now find the change in length:
ΔL = αLΔT = (2.00 × 10^-5/C°) × (40.00 mm) × (-100°C) = -0.080 mm

The change in diameter is:
ΔD = 2ΔL = 2 × (-0.080 mm) = -0.160 mm

The final diameter is:
D = 80.00 mm + ΔD = 80.00 mm - 0.160 mm = 79.840 mm

Therefore, the answer is D.

The Stanford Linear Accelerator Contains Hundreds of Brass Disks Tightly °\degree°

The Stanford Linear Accelerator Contains Hundreds of Brass Disks Tightly $\degree$