Coefficient of Linear Expansion in Fahrenheit vs Kelvin: How Does the Numerical Value Change?

When discussing the coefficient of linear expansion, it’s important to consider the temperature scale being used. This coefficient, often expressed in units of per K (per Kelvin) or per °F (per degree Fahrenheit), indicates how much a material expands per degree rise in temperature. This article will explore how the numerical value of the coefficient of linear expansion changes when the unit of measurement is converted from per K to per °F.

Understanding the Coefficient of Linear Expansion

The coefficient of linear expansion, denoted as α, is a key parameter that describes how a material’s length changes in response to a change in temperature. It can be expressed as follows:

In per K (per Kelvin): [ alpha , text{per K}] In per °F (per degree Fahrenheit): [ alpha , text{per °F}]

Conversion Between Kelvin and Fahrenheit

When converting between these two temperature scales, it’s crucial to understand the relationship between Kelvin and Fahrenheit. While one degree Celsius (°C) is equivalent to one Kelvin (K), a change of 1 °F (degree Fahrenheit) corresponds to a change of (frac{5}{9}) °C or (frac{5}{9}) K. This relationship is vital for converting the numerical value of the coefficient of linear expansion between the two units.

Conversion Factor Between Kelvin and Fahrenheit

To convert from per K to per °F, use the following conversion factor:

[1 , text{K} frac{9}{5} , text{°F}]

Consequently, to convert the coefficient of linear expansion from per K to per °F, multiply by (frac{9}{5}).

Example Conversion

Let's consider an example to illustrate this concept. Assume that the coefficient of linear expansion for a material is [alpha 1.2 times 10^{-4} , text{per °F}]. We can convert this value to per °C (or K) as follows:

Substitute the conversion factor from °F to °C: [1 , text{°F} frac{5}{9} , text{°C}] 2. Multiply the given coefficient by this conversion factor to get the equivalent value in per °C (K): [1.2 times 10^{-4} , text{per °F} 1.2 times 10^{-4} times frac{9}{5} , text{per °C}] 3. Simplify the expression: [1.2 times 10^{-4} , text{per °F} 2.16 times 10^{-4} , text{per °C}]

Why the Numerical Value Changes

It’s important to note that the numerical value changes when converting from per K to per °F because the size of a degree in Fahrenheit is not the same as a degree in Kelvin or Celsius. This change in the value reflects the different sizes of the temperature units involved.

The coefficient of linear expansion (alpha) is a combination of a numerical value and a unit. When the unit changes, the numerical value changes to maintain the integrity of the coefficient. This is because the physical property being measured (the rate of expansion) remains constant, but the units used to express it differ.

Conclusion

In summary, the numerical value of the coefficient of linear expansion changes when converting from per K to per °F due to the different sizes of temperature units in these scales. The conversion factor of (frac{9}{5}) is essential for accurate and consistent measurements in both units. Understanding this relationship is crucial for applications in materials science, engineering, and related fields that involve temperature-induced dimensional changes.