Question

What is \(-15^{\circ} \mathrm{F}\) in degrees Celsius and in kelvins?

Short answer

-15°F is -26.1°C and 247.05K.

Step-by-step solution

Understand the Fahrenheit to Celsius Conversion Formula

The formula to convert Fahrenheit to Celsius is given by: \[ C = \frac{5}{9}(F - 32) \]Where \(C\) is the temperature in degrees Celsius and \(F\) is the temperature in degrees Fahrenheit.

Substitute the Given Temperature

Substitute \( -15 \) for \( F \) (degrees Fahrenheit) into the conversion formula: \[ C = \frac{5}{9}(-15 - 32) \]

Simplify Inside the Parentheses

First, subtract 32 from -15: \[ -15 - 32 = -47 \]So, the expression becomes: \[ C = \frac{5}{9}(-47) \]

Multiply and Simplify

Now, multiply \( \frac{5}{9} \times -47 \): \[ \frac{5 \times -47}{9} = \frac{-235}{9} = -26.1 \]Thus, \[ C = -26.1^{\text{o}} \text{C} \]

Convert Celsius to Kelvins

To convert from Celsius to Kelvin, use the formula: \[ K = C + 273.15 \]Substitute \( C = -26.1 \): \[ K = -26.1 + 273.15 = 247.05 \text{K} \]

Key concepts

Fahrenheit to Celsius conversion

When we need to convert a temperature from Fahrenheit to Celsius, a specific mathematical formula is used. The formula is \(\text{C} = \frac{5}{9} (\text{F} - 32)\). The symbol \(C\) stands for degrees Celsius and \(F\) stands for degrees Fahrenheit.

To break it down further, let's look at an example. Say you have \(-15 \degree \text{F}\) (degrees Fahrenheit) and want to find what that is in Celsius. You just need to substitute \-15\ for \(F\) in the formula:
\[ \text{C} = \frac{5}{9} (-15 - 32) \]
First, subtract 32 from -15: \(-15 - 32 = -47\). This gives us:
\[ \text{C} = \frac{5}{9} (-47) \]
Now, multiply \( \frac{5}{9} \times -47 \):
\[ \frac{5 \times -47}{9} = \frac{-235}{9}\] \ \[ = -26.1\] \
Thus, \(-15 \degree \text{F}\) is \(-26.1 \degree \text{C}\).

Celsius to Kelvin conversion

To convert a temperature from Celsius to Kelvin, a simple addition is used. The formula is \[ K = C + 273.15 \]. Here, \(K\) represents the temperature in Kelvins and \(C\) is the temperature in degrees Celsius.

For example, if you have \(-26.1 \degree \text{C}\) (from our previous calculation), and you want to convert it to Kelvin, just add 273.15 to the Celsius temperature:

\[ K = -26.1 + 273.15 = 247.05 \]
Therefore, \(-26.1 \degree \text{C}\) is equal to 247.05 Kelvins.

temperature calculations

Understanding how to perform temperature calculations involves knowing how to convert between different temperature scales and managing the basic arithmetic involved.

For instance, converting Fahrenheit to Celsius involves using the formula \[ \text{C} = \frac{5}{9} (\text{F} - 32) \]. It's important to first handle the subtraction in the parentheses before performing the multiplication.

• Subtract 32 from the Fahrenheit value.
• Multiply the result by \( \frac{5}{9} \).

After finding the Celsius value, converting it to Kelvin is straightforward using the formula \[ K = C + 273.15 \]. You are adding 273.15 to the Celsius temperature.

With these steps, you can efficiently convert between Fahrenheit, Celsius, and Kelvin, tackling a variety of temperature-related problems.