A U.S. penny has a diameter of 1.9000 cm at 20.0^. The coin is made of a metal alloy (mostly zin

step 1 So we want to find how the diameter would change based on it being placed in two locations. So w

A U.S. penny has a diameter of 1.9000 cm at 20.0^. The coin...

A U.S. penny has a diameter of 1.9000 cm at 20.0$^\circ$C. The coin is made of a metal alloy (mostly zinc) for which the coefficient of linear expansion is $2.6 \times 10{^-}{^5} K{^-}{^1}$. What would its diameter be on a hot day in Death Valley (48.0$^\circ$C)? On a cold night in the mountains of Greenland (-53$^\circ$C)?

Key Concepts

Linear Expansion Equation

The linear expansion equation, given by L = L? (1 + ??T), relates the initial dimension (L?) of an object to its new dimension (L) after a temperature change. Here, ? is the coefficient of linear expansion and ?T is the temperature change. This equation is essential for calculating how much a dimension, such as the diameter of a coin, will increase or decrease with temperature variations.

Temperature Change (?T)

Temperature change, often represented as ?T, is the difference between the final and initial temperatures. In the context of thermal expansion, this value is crucial because it directly influences the degree to which the material's dimensions will change, according to the material's expansion coefficient.

Coefficient of Linear Expansion

The coefficient of linear expansion is a material-specific constant that describes how much a material's length (or other linear dimension) changes per degree change in temperature. It is typically expressed in units of inverse temperature (such as K?¹ or °C?¹) and allows for predicting the change in dimension for a given temperature variation.

Thermal Expansion

Thermal expansion refers to the tendency of matter, particularly solids, liquids, and gases, to change in shape, area, and volume in response to a change in temperature. In solids, this change is usually small and can be quantified by measuring the change in a specific dimension, such as length or diameter, as the material heats up or cools down.

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