# Thermal Expansion of a steel plate

• Brit412
In summary, the problem involves a steel plate with a circular hole and a Pyrex glass marble of different diameters. The question asks for the temperature change needed in order for the marble to fit through the hole. The solution involves using the equation ∆L = alpha L(0) ∆T for both the plate and the marble. The book's answer is 350, while the steps outlined in the conversation lead to a temperature change of 345.2.
Brit412

## Homework Statement

A steel plate has a circular hole with a diameter of 1.000 cm. In order to drop a Pyrex glass marble 1.003 cm in diameter through the hole in the plate, how much must the temperature of the system be raised? (Assume the plate and the marble always have the same temperature)

## Homework Equations

∆L= alpha L(0) ∆T

## The Attempt at a Solution

Use the above equation for both the marble and plate, but I don't know what temperature to use for ∆T

it doesn't matter what temperature it starts at, DELTA T is just the change in temperature, so if it went from 0 to 10 or 900 to 910 DELTA T would still be 10.

I'm still confused. The book says the answer is 350 but I don't see how they arrived at that answer. Here's what I did so far:

∆L (plate) = (12E-6) times (0.01m)
∆L (marble) = (3.3E-6) times (0.01003m)

so, the difference in length between the P and the M is .00003m.
so what youre looking for will be the temperature at which the ∆Lp is different by ∆m by .00003m. (since when the plate is .00003 meters bigger, the marble will fit through.)

so ∆Lp-.00003m = ∆m
(it is minus the difference because you really want the plate to be .00003m bigger, so if you substract it, it would make the terms equal
then you can plug in for the rest
(∆T(12E-6)(.01))-.0003=∆T(3.3E-6)(.01003)
and factor out the T, and it will leave you with ∆T=345.2

Thank you so much for helping me understand that problem

## What is thermal expansion?

Thermal expansion is the tendency of a material to expand or contract in response to changes in temperature.

## Why does steel plate experience thermal expansion?

Steel is made up of atoms that vibrate more vigorously at higher temperatures, causing the material to expand. This is due to the increase in kinetic energy of the atoms.

## How does thermal expansion affect the dimensions of a steel plate?

Thermal expansion causes the steel plate to increase in size as it absorbs heat and decrease in size as it cools down. This can lead to changes in the dimensions of the plate, which can be significant in industrial applications.

## What factors can affect the degree of thermal expansion in a steel plate?

The degree of thermal expansion in a steel plate can be affected by factors such as the temperature change, the type and composition of the steel, and the shape and size of the plate.

## How can thermal expansion of a steel plate be managed or controlled?

Thermal expansion of a steel plate can be managed or controlled by using materials with lower coefficients of thermal expansion, incorporating expansion joints to allow for movement, and designing structures with enough flexibility to accommodate thermal expansion.

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