The active element of a certain laser is made of a glass rod 30.0 cm long and 1.50 cm in diamete

step 1 We are looking at the expansion of a glass rod inside of a laser with a temperature change of 65

The active element of a certain laser is made of a glass rod...

The active element of a certain laser is made of a glass rod 30.0 $\mathrm{cm}$ long and 1.50 $\mathrm{cm}$ in diameter. Assume the average coefficient of linear expansion of the glass is equal to $9.00 \times 10^{-6}\left(^{\circ} \mathrm{C}\right)^{-1}$ . If the temperature of the rod increases by $65.0^{\circ} \mathrm{C},$ what is the increase in (a) its length, (b) its diameter, and (c) its volume?

The active element of a certain laser is made of a glass rod 30.0 $\mathrm{cm}$ long and
1.50 $\mathrm{cm}$ in diameter. Assume the average coefficient of linear expansion of the glass is equal to $9.00 \times 10^{-6}\left(^{\circ} \mathrm{C}\right)^{-1}$ . If the temperature of the rod increases by $65.0^{\circ} \mathrm{C},$ what is the increase in (a) its length, (b) its diameter, and (c) its volume?

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Key Concepts

Thermal Expansion

Thermal expansion is the tendency of matter to change its dimensions in response to changes in temperature. When a material is heated, its atoms vibrate more intensely and tend to move slightly apart, resulting in an increase in the overall dimensions of the object. This concept is fundamental for understanding how changes in temperature can affect the size and volume of objects across various applications.

Coefficient of Linear Expansion

The coefficient of linear expansion, denoted by ?, measures how much a material’s length changes per degree change in temperature. It is defined as the fractional change in length per unit temperature and is used to calculate the increase or decrease in any linear dimension, such as the length or diameter of a rod, when the temperature is varied.

Volume Thermal Expansion

Volume thermal expansion describes how the overall volume of a material changes in response to temperature variations. For isotropic materials that expand equally in all directions, the volumetric expansion coefficient is approximately three times the linear expansion coefficient for small temperature changes. This concept helps in determining how the total volume of an object, such as a cylindrical rod, will change with temperature.

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