A piece of aluminum has a volume of 1.4 ×10^-3 m^3 . The coefficient of volume expansion for alu

step 1 temperature of aluminum is raised from 20 degrees Celsius to 320 degrees Celsius and initial vol

A piece of aluminum has a volume of 1.4 ×10^-3 m^3 . The...

A piece of aluminum has a volume of $1.4 \times 10^{-3} \mathrm{m}^{3} .$ The coefficient of volume expansion for aluminum is $\beta=69 \times 10^{-6}\left(\mathrm{C}^{\circ}\right)^{-1}$ . The temperature of this object is raised from 20 to $320^{\circ} \mathrm{C} .$ How much work is done by the expanding aluminum if the air pressure is $1.01 \times 10^{5} \mathrm{Pa} ?$

A piece of aluminum has a volume of $1.4 \times 10^{-3} \mathrm{m}^{3} .$ The coefficient of volume expansion for aluminum is $\beta=69 \times 10^{-6}\left(\mathrm{C}^{\circ}\right)^{-1}$ . The temperature of this object is raised from 20 to $320^{\circ} \mathrm{C} .$ How much work is
done by the expanding aluminum if the air pressure is $1.01 \times 10^{5} \mathrm{Pa} ?$

Key Concepts

Coefficient of Thermal Expansion

The coefficient of thermal expansion quantifies how much a material’s dimensions change per degree change in temperature. It is a material-specific property that relates temperature difference to the fractional change in length, area, or volume, and it is essential in predicting how materials behave under thermal stress.

Volumetric Thermal Expansion

Volumetric thermal expansion describes the change in a material’s volume in response to a temperature change. It is typically calculated by multiplying the original volume by the volumetric coefficient of expansion and the temperature difference, allowing us to understand and predict the expansion behavior of solids, liquids, or gases when heated.

Work Done by Expansion

Work done by an expanding material under pressure is determined by the product of the pressure and the change in volume (W = P?V). This concept is fundamental in thermodynamics, as it connects mechanical work with the energy change associated with the physical expansion of a material against an external pressure.

Effect of Constant External Pressure

In problems where the expanding material is subject to a constant external pressure, such as atmospheric pressure, the calculation of work is simplified. The constant pressure allows for a straightforward computation of work done by the material as it expands, thereby linking thermal changes to mechanical energy outputs.

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