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.

This comparison confirms that X = 32.

Revision Table: Temperature Scales

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.