The formula for conversion between Fahrenheit and Celsius is °F = X + (1⋅8 × °C)
32
Understanding Temperature Conversion Formula
The question asks us to identify the factor X in the given formula for converting temperature from Celsius (°C) to Fahrenheit (°F). The formula provided is:
\(\) \text{°F} = \text{X} + (1.8 \times \text{°C}) \(\)
Standard Celsius to Fahrenheit Conversion
The standard and widely accepted formula for converting a temperature from the Celsius scale to the Fahrenheit scale is:
\(\) \text{°F} = \left(\frac{9}{5} \times \text{°C}\right) + 32 \(\)
We know that the fraction \(\frac{9}{5}\) is equal to the decimal value 1.8.
So, the standard formula can also be written as:
\(\) \text{°F} = (1.8 \times \text{°C}) + 32 \(\)
Identifying Factor X
Now, let's compare the given formula with the standard formula:
- Given Formula: \(\) \text{°F} = \text{X} + (1.8 \times \text{°C}) \(\)
- Standard Formula: \(\) \text{°F} = 32 + (1.8 \times \text{°C}) \(\) (rearranging the standard formula slightly to match the structure)
By comparing these two formulas, we can see that the structure is the same, and the coefficient for °C is 1.8 in both cases. The constant term that is added to the result of \((1.8 \times \text{°C})\) is X in the given formula and 32 in the standard formula.
Therefore, by direct comparison, the factor X must be equal to 32.
Comparing Options for Factor X
Let's look at the provided options:
- Option 1: 32
- Option 2: 22
- Option 3: 98
- Option 4: 42
Our derived value for factor X is 32, which matches Option 1.
| Component | Given Formula | Standard Formula |
|---|---|---|
| Temperature in Fahrenheit (°F) | °F | °F |
| Temperature in Celsius (°C) | °C | °C |
| Multiplication Factor for °C | 1.8 | 1.8 (from 9/5) |
| Added Constant | X | 32 |
This comparison confirms that X = 32.
Revision Table: Temperature Scales
| Scale | Symbol | Freezing Point of Water | Boiling Point of Water |
|---|---|---|---|
| Celsius | °C | 0°C | 100°C |
| Fahrenheit | °F | 32°F | 212°F |
| Kelvin | K | 273.15 K (approx) | 373.15 K (approx) |
Additional Information: Temperature Conversion Factors
Temperature conversion is a common operation in physics and everyday life. The relationship between different temperature scales is linear.
The formula \(\text{°F} = \left(\frac{9}{5} \times \text{°C}\right) + 32\) can be rearranged to convert Fahrenheit to Celsius:
\(\) \text{°F} - 32 = \frac{9}{5} \times \text{°C} \(\)
\(\) \text{°C} = \frac{5}{9} \times (\text{°F} - 32) \(\)
Conversions involving Kelvin (K) are also important. Kelvin is an absolute scale, meaning 0 K is absolute zero.
- Celsius to Kelvin: \(\) \text{K} = \text{°C} + 273.15 \(\)
- Kelvin to Celsius: \(\) \text{°C} = \text{K} - 273.15 \(\)
Fahrenheit to Kelvin conversions usually go via Celsius first.
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