A steel plate has a circular hole with a diameter of 1.000 cm . In order to drop a Pyrex glass m

step 1 In this problem, I will use the formula of the temperature change that is d 'al t is equal to L

A steel plate has a circular hole with a diameter of 1.000...

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

Key Concepts

Thermal Expansion

Thermal expansion is the tendency of matter to change its dimensions in response to a change in temperature. When heated, materials typically expand, and the amount by which they do so is dependent on the material’s intrinsic properties and the temperature change. This concept is crucial in understanding how the dimensions of both the steel plate and the Pyrex marble change as the temperature increases.

Coefficient of Linear Expansion

The coefficient of linear expansion is a material-specific factor that quantifies the fractional change in length (or diameter) per unit temperature change. It allows us to calculate how much a given dimension will change when the material is heated or cooled. In problems involving objects of different materials, such as a steel plate and a Pyrex marble, knowing the individual coefficients is essential to predicting their relative expansions.

Differential Expansion

Differential expansion refers to the differing amounts by which two materials expand upon heating due to their distinct coefficients of thermal expansion. When two objects with different expansion rates are at the same temperature, their dimensions change by different amounts, which can result in a change in the clearance or fit between them. This concept is key to determining how much the temperature must be raised for an expanded opening (in the steel plate) to accommodate an expanded object (the Pyrex marble).

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