SOLUTION: Temperature conversion - Studypool - Free Printable

Problem Overview:

The task involves converting temperatures between different temperature scales: Fahrenheit (°F), Celsius (°C), and Kelvin (K). The provided formulas are:

1. Fahrenheit to Celsius:
\[
C = \frac{5}{9}(F - 32)
\]

2. Celsius to Fahrenheit:
\[
F = \frac{9}{5}C + 32
\]

3. Celsius to Kelvin:
\[
K = C + 273.15
\]

4. Kelvin to Celsius:
\[
C = K - 273.15
\]

We will solve each conversion step-by-step using these formulas.

---

Conversions to Fahrenheit (°F):

#### 1. \( 0^\circ \text{C} \) to °F:
\[
F = \frac{9}{5}C + 32
\]
Substitute \( C = 0 \):
\[
F = \frac{9}{5}(0) + 32 = 0 + 32 = 32
\]
Answer: \( 32^\circ \text{F} \)

#### 2. \( 10^\circ \text{C} \) to °F:
\[
F = \frac{9}{5}C + 32
\]
Substitute \( C = 10 \):
\[
F = \frac{9}{5}(10) + 32 = 18 + 32 = 50
\]
Answer: \( 50^\circ \text{F} \)

#### 3. \( 20^\circ \text{C} \) to °F:
\[
F = \frac{9}{5}C + 32
\]
Substitute \( C = 20 \):
\[
F = \frac{9}{5}(20) + 32 = 36 + 32 = 68
\]
Answer: \( 68^\circ \text{F} \)

#### 4. \( 30^\circ \text{C} \) to °F:
\[
F = \frac{9}{5}C + 32
\]
Substitute \( C = 30 \):
\[
F = \frac{9}{5}(30) + 32 = 54 + 32 = 86
\]
Answer: \( 86^\circ \text{F} \)

#### 5. \( 40^\circ \text{C} \) to °F:
\[
F = \frac{9}{5}C + 32
\]
Substitute \( C = 40 \):
\[
F = \frac{9}{5}(40) + 32 = 72 + 32 = 104
\]
Answer: \( 104^\circ \text{F} \)

---

Conversions to Kelvin (K):

#### 6. \( 25^\circ \text{C} \) to K:
\[
K = C + 273.15
\]
Substitute \( C = 25 \):
\[
K = 25 + 273.15 = 298.15
\]
Answer: \( 298.15 \, \text{K} \)

#### 7. \( 35^\circ \text{C} \) to K:
\[
K = C + 273.15
\]
Substitute \( C = 35 \):
\[
K = 35 + 273.15 = 308.15
\]
Answer: \( 308.15 \, \text{K} \)

#### 8. \( 45^\circ \text{C} \) to K:
\[
K = C + 273.15
\]
Substitute \( C = 45 \):
\[
K = 45 + 273.15 = 318.15
\]
Answer: \( 318.15 \, \text{K} \)

#### 9. \( 55^\circ \text{C} \) to K:
\[
K = C + 273.15
\]
Substitute \( C = 55 \):
\[
K = 55 + 273.15 = 328.15
\]
Answer: \( 328.15 \, \text{K} \)

#### 10. \( 65^\circ \text{C} \) to K:
\[
K = C + 273.15
\]
Substitute \( C = 65 \):
\[
K = 65 + 273.15 = 338.15
\]
Answer: \( 338.15 \, \text{K} \)

---

Conversions to Celsius (°C):

#### 11. \( 32^\circ \text{F} \) to °C:
\[
C = \frac{5}{9}(F - 32)
\]
Substitute \( F = 32 \):
\[
C = \frac{5}{9}(32 - 32) = \frac{5}{9}(0) = 0
\]
Answer: \( 0^\circ \text{C} \)

#### 12. \( 50^\circ \text{F} \) to °C:
\[
C = \frac{5}{9}(F - 32)
\]
Substitute \( F = 50 \):
\[
C = \frac{5}{9}(50 - 32) = \frac{5}{9}(18) = 10
\]
Answer: \( 10^\circ \text{C} \)

#### 13. \( 68^\circ \text{F} \) to °C:
\[
C = \frac{5}{9}(F - 32)
\]
Substitute \( F = 68 \):
\[
C = \frac{5}{9}(68 - 32) = \frac{5}{9}(36) = 20
\]
Answer: \( 20^\circ \text{C} \)

#### 14. \( 86^\circ \text{F} \) to °C:
\[
C = \frac{5}{9}(F - 32)
\]
Substitute \( F = 86 \):
\[
C = \frac{5}{9}(86 - 32) = \frac{5}{9}(54) = 30
\]
Answer: \( 30^\circ \text{C} \)

#### 15. \( 104^\circ \text{F} \) to °C:
\[
C = \frac{5}{9}(F - 32)
\]
Substitute \( F = 104 \):
\[
C = \frac{5}{9}(104 - 32) = \frac{5}{9}(72) = 40
\]
Answer: \( 40^\circ \text{C} \)

---

Conversions from Kelvin to Celsius:

#### 16. \( 273.15 \, \text{K} \) to °C:
\[
C = K - 273.15
\]
Substitute \( K = 273.15 \):
\[
C = 273.15 - 273.15 = 0
\]
Answer: \( 0^\circ \text{C} \)

#### 17. \( 298.15 \, \text{K} \) to °C:
\[
C = K - 273.15
\]
Substitute \( K = 298.15 \):
\[
C = 298.15 - 273.15 = 25
\]
Answer: \( 25^\circ \text{C} \)

#### 18. \( 308.15 \, \text{K} \) to °C:
\[
C = K - 273.15
\]
Substitute \( K = 308.15 \):
\[
C = 308.15 - 273.15 = 35
\]
Answer: \( 35^\circ \text{C} \)

#### 19. \( 318.15 \, \text{K} \) to °C:
\[
C = K - 273.15
\]
Substitute \( K = 318.15 \):
\[
C = 318.15 - 273.15 = 45
\]
Answer: \( 45^\circ \text{C} \)

#### 20. \( 328.15 \, \text{K} \) to °C:
\[
C = K - 273.15
\]
Substitute \( K = 328.15 \):
\[
C = 328.15 - 273.15 = 55
\]
Answer: \( 55^\circ \text{C} \)

---

Final Answers:

\[
\boxed{
\begin{array}{ll}
1. & 32^\circ \text{F} \\
2. & 50^\circ \text{F} \\
3. & 68^\circ \text{F} \\
4. & 86^\circ \text{F} \\
5. & 104^\circ \text{F} \\
6. & 298.15 \, \text{K} \\
7. & 308.15 \, \text{K} \\
8. & 318.15 \, \text{K} \\
9. & 328.15 \, \text{K} \\
10. & 338.15 \, \text{K} \\
11. & 0^\circ \text{C} \\
12. & 10^\circ \text{C} \\
13. & 20^\circ \text{C} \\
14. & 30^\circ \text{C} \\
15. & 40^\circ \text{C} \\
16. & 0^\circ \text{C} \\
17. & 25^\circ \text{C} \\
18. & 35^\circ \text{C} \\
19. & 45^\circ \text{C} \\
20. & 55^\circ \text{C} \\
\end{array}
}
\]