A brass lid screws tightly onto a glass jar at 20 degrees C. To help open the jar, it can be placed into a bath of hot water. Af

Question

3 months ago

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A brass lid screws tightly onto a glass jar at 20 degrees C. To help open the jar, it can be placed into a bath of hot water. Af

ter this treatment, the temperature of the lid and the jar are both 60 degrees C. The inside diameter of the lid is 8.0 cm at 20 degrees C. Find the size of the gap (difference in radius) that develops by this procedure.

Physics

1 answer:

serg [3.5K] · Answer 1 · 2026-03-07T11:38:00+03:00

Answer:

0.0016 cm

Explanation:

$\alpha_b$ = The thermal expansion coefficient for brass = $19\times 10^{-6}\ /^{\circ}C$

$\alpha_g$ = The thermal expansion coefficient for glass = $9\times 10^{-6}\ /^{\circ}C$

$\Delta T$ = Temperature change = $(60-20)^{\circ}C$

$R_0$ = Original radius = 4 cm

The change in radius is described by

$R=R_0(1+\alpha\Delta T)$

The radius difference between the lid and the jar

$\Delta R=R_b-R_g\\\Rightarrow \Delta R=R_0(1+\alpha_b\Delta T)-R_0(1+\alpha_g\Delta T)\\\Rightarrow \Delta R=R_0(\alpha_b-\alpha_g)\Delta T\\\Rightarrow \Delta R=4\times (19\times 10^{-6}-9\times 10^{-6})\times (60-20)\\\Rightarrow \Delta R=0.0016\ cm$

The gap measures 0.0016 cm or 0.000016 m