Certainly! Let's address the two parts of the question step-by-step:
### Part 1: Changing the Unit of Coefficient of Linear Expansion
When converting the unit of the coefficient of linear expansion from per Kelvin ([tex]\(\text{K}^{-1}\)[/tex]) to per Fahrenheit ([tex]\(\text{°F}^{-1}\)[/tex]), we need to consider the relationship between the Kelvin and Fahrenheit scales.
1. Understanding Units of Temperature Expansion:
- The Kelvin scale and Celsius scale have the same incremental size; a change of 1 °C is equivalent to a change of 1 K.
- The Fahrenheit scale is related to the Celsius scale by the equation: [tex]\(^\circ\)[/tex]F = [tex]\(^\circ\)[/tex]C 1.8 + 32.
2. Transforming the Unit:
- To convert from per Kelvin to per Fahrenheit, we need to account for the difference in scale. The factor here is 1.8 because each degree change in Celsius (or Kelvin) corresponds to a 1.8-degree change in Fahrenheit.
3. Conversion Factor:
- The conversion factor from per K to per °F is the reciprocal of 1.8 (since [tex]\(^\circ\)[/tex]F = [tex]\(^\circ\)[/tex]C 1.8). This means:
[tex]\[
\text{Conversion Factor} = \frac{1}{1.8} \approx 0.5556
\][/tex]
Thus, when the unit of the coefficient of linear expansion is changed from per K to per °F, the numerical value does indeed change. Specifically, it is multiplied by approximately 0.5556.
### Part 2: Temperature Conversion from Celsius to Kelvin
To convert a temperature from Celsius to Kelvin, we use the following relationship:
[tex]\[
\text{K} = \text{°C} + 273.15
\][/tex]
Given a room temperature of 30 °C:
[tex]\[
\text{Room temperature in Kelvin} = 30 + 273.15 = 303.15 \, \text{K}
\][/tex]
### Summary
- The numerical value of the coefficient of linear expansion does change when the unit is converted from per K to per °F. It is scaled by approximately 0.5556.
- The room temperature of 30 °C is equivalent to 303.15 K on the Kelvin scale.
Therefore, the results are:
[tex]\[
\text{Conversion factor} \approx 0.5556, \quad \text{Room temperature} = 303.15 \, \text{K}
\][/tex]
I hope this helps clarify the steps involved in solving the problem!
