https://file.aiquickdraw.com/mathbot/file/1724857475733662sazgk.jpg

Convert these equations from Fahrenheit to Celsius and then to kelvin

The image contains a series of equations for converting temperatures from Fahrenheit to Celsius and then to Kelvin. I'll go through each conversion process.

### 1. Conversion Equations:
The general equations used for temperature conversion are:
- **Celsius (°C) from Fahrenheit (°F):**
  \[
  \text{°C} = \frac{5}{9} (\text{°F} - 32)
  \]
- **Kelvin (K) from Celsius (°C):**
  \[
  \text{K} = \text{°C} + 273.15
  \]

### 2. Detailed Steps:
Let's apply these to the specific values mentioned in your image.

#### (a) For \( 320^\circ \text{F} \):
1. Convert to Celsius:
   \[
   \text{°C} = \frac{5}{9}(320 - 32) = \frac{5}{9}(288) \approx 160^\circ \text{C}
   \]
2. Convert to Kelvin:
   \[
   \text{K} = 160 + 273.15 \approx 433.15 \, \text{K}
   \]

#### (b) For \( 0.2^\circ \text{F} \):
1. Convert to Celsius:
   \[
   \text{°C} = \frac{5}{9}(0.2 - 32) = \frac{5}{9}(-31.8) \approx -17.67^\circ \text{C}
   \]
2. Convert to Kelvin:
   \[
   \text{K} = -17.67 + 273.15 \approx 255.48 \, \text{K}
   \]

#### (c) For \( -250^\circ \text{F} \):
1. Convert to Celsius:
   \[
   \text{°C} = \frac{5}{9}(-250 - 32) = \frac{5}{9}(-282) \approx -156.67^\circ \text{C}
   \]
2. Convert to Kelvin:
   \[
   \text{K} = -156.67 + 273.15 \approx 116.48 \, \text{K}
   \]

### Summary:
1. \( 320^\circ \text{F} \approx 160^\circ \text{C} \approx 433.15 \, \text{K} \)
2. \( 0.2^\circ \text{F} \approx -17.67^\circ \text{C} \approx 255.48 \, \text{K} \)
3. \( -250^\circ \text{F} \approx -156.67^\circ \text{C} \approx 116.48 \, \text{K} \)

Would you like further details or have any questions?

### Related Questions:
1. How would you convert from Kelvin to Fahrenheit directly?
2. Why is it necessary to add 273.15 when converting from Celsius to Kelvin?
3. How do significant figures affect temperature conversions?
4. What are the physical implications of temperatures below 0°C in Kelvin?
5. Can the Kelvin scale have negative values? Why or why not?

### Tip:
Always keep track of significant figures throughout the calculation to ensure precision in your results.

Learn how to convert temperatures from Fahrenheit to Celsius and then to Kelvin using detailed conversion equations and examples. Understand the formulas °C = (5/9) (°F - 32) and K = °C + 273.15 with step-by-step solutions for specific temperature values.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation