18-2 The Celsius and Fahrenheit Scales

18-2 The Celsius and Fahrenheit Scales#

Prompts

  • How is the Celsius scale related to the Kelvin scale? What is 0°C in kelvins? What is the size of one Celsius degree compared to one kelvin?

  • Write the conversion formula from Celsius to Fahrenheit. At what temperature do the two scales read the same number?

  • Convert 98.6°F (body temperature) to Celsius and Kelvin.

  • What is the difference between “20°C” and “20 C°”? Why does this distinction matter?

Lecture Notes#

Overview#

  • The Celsius and Fahrenheit scales are practical temperature scales derived from the Kelvin scale (section 18-1).

  • Celsius: same degree size as Kelvin; zero shifted to a convenient value (water freezing point).

  • Fahrenheit: smaller degree; different zero. Conversion between scales is linear.

Celsius scale#

The Celsius scale is defined by shifting the Kelvin zero:

(150)#\[ T_C = T - 273.15 \]

  • \(T\) in kelvins; \(T_C\) in degrees Celsius (°C).

  • One Celsius degree has the same size as one kelvin: \(\Delta T_C = \Delta T\).

  • 0°C = 273.15 K (freezing point of water at 1 atm); 100°C ≈ 373.15 K (boiling point).

Fahrenheit scale#

The Fahrenheit scale relates to Celsius by

(151)#\[ T_F = \frac{9}{5}T_C + 32 \]

  • \(T_F\) in degrees Fahrenheit (°F).

  • One Fahrenheit degree is smaller than one Celsius degree: 5 C° = 9 F°.

  • 0°C = 32°F; 100°C = 212°F.

  • Inverse: \(T_C = \frac{5}{9}(T_F - 32)\).

Reference

°C

°F

Boiling point of water

100

212

Freezing point of water

0

32

Scales coincide

−40

−40

Absolute zero

−273.15

−459.67

Global usage of temperature scales

Fahrenheit is used mainly in the United States for everyday weather and household temperature. Most of the world uses Celsius. In science, Celsius and Kelvin are the standard units of temperature (Kelvin in SI).

Temperature vs temperature difference#

  • 0°C = a specific temperature (freezing point).

  • 5 C° = a temperature difference of 5 Celsius degrees.

  • For a change: \(\Delta T_C = \Delta T\) (kelvins); \(\Delta T_F = \frac{9}{5}\Delta T_C\).

Poll: Temperature scale degree size

The figure shows three temperature scales (X, Y, Z) with the freezing and boiling points of water indicated. What is biggest: a temperature increase of 10°X, 10°Y, or 10°Z?

[FIGURE: Three temperature scales with freezing and boiling points of water marked; show that degree sizes differ—e.g., X has smallest degrees, Z has largest]

  • (A) 10°X

  • (B) 10°Y

  • (C) 10°Z

  • (D) Two or more tie for the biggest increase

Poll: Conversion

Room temperature is about 20°C. What is it in Fahrenheit?

  • (A) 36°F

  • (B) 52°F

  • (C) 68°F

Summary#

  • \(T_C = T - 273.15\)—Celsius from Kelvin; 1 C° = 1 K.

  • \(T_F = \frac{9}{5}T_C + 32\)—Fahrenheit from Celsius.

  • \(T_C = \frac{5}{9}(T_F - 32)\)—Celsius from Fahrenheit.

  • 5 C° = 9 F° for temperature differences.