Question

On which temperature scale \((\mathrm{F}, \mathrm{C},\) or \(\mathrm{K})\) does 1 degree represent the smallest change in temperature?

Short answer

The temperature scales with the smallest change in temperature for 1 degree are Celsius (C) and Kelvin (K), as both of these scales have a 1-degree change representing the smallest change in temperature when compared to the 1.8-degree change in Fahrenheit.

Step-by-step solution

Understand the conversions between different temperature scales

The relationship between the Fahrenheit, Celsius, and Kelvin temperature scales can be represented using the following formulas: \(C = (F-32)\times\frac{5}{9}\) - Conversion from Fahrenheit to Celsius \(F = C\times\frac{9}{5} + 32\) - Conversion from Celsius to Fahrenheit \(K = C + 273.15\) - Conversion from Celsius to Kelvin \(C = K - 273.15\) - Conversion from Kelvin to Celsius

Compare the conversion rates for Fahrenheit and Celsius

Let's take an example where a temperature difference of 1 degree Celsius (ΔC = 1) and then convert it into Fahrenheit scale. ΔF = ΔC × (9/5) ΔF = 1 × (9/5) ΔF = 9/5 = 1.8 There is a 1.8-degree Fahrenheit change for every 1-degree Celsius change.

Compare the conversion rates for Celsius and Kelvin

Kelvin and Celsius have the same magnitude of change, with only an offset of 273.15. Hence, a 1-degree change in temperature is equal to a 1-degree change in both Celsius and Kelvin. In simpler terms, if ΔC = 1, then ΔK = 1.

Determine the smallest temperature change

Comparing the conversions, we have: ΔF = 1.8 (from Fahrenheit to Celsius) ΔC = 1 (from Celsius to Kelvin or vice versa) Since the change in Celsius and Kelvin is smaller than the change in Fahrenheit, the temperature scale with the smallest change in temperature is the Celsius (C) or Kelvin (K) scale. Both of these scales have a 1-degree change representing the smallest change in temperature.

Key concepts

Fahrenheit

The Fahrenheit scale is a temperature measurement system commonly used in the United States. Created by Daniel Gabriel Fahrenheit in the early 18th century, it sets the freezing point of water at 32 degrees and the boiling point at 212 degrees under standard atmospheric pressure.
This results in 180 degrees between these two points.

• Freezing point of water: 32°F
• Boiling point of water: 212°F

Compared to Celsius and Kelvin, the Fahrenheit scale reflects a smaller change in temperature for each degree. When you convert a 1-degree Celsius change to Fahrenheit, it translates to a 1.8-degree change. This means that each degree on the Fahrenheit scale is a bit smaller compared to the other scales. This characteristic is why the changes on the Fahrenheit scale appear larger when comparing similar Celsius or Kelvin changes.

Celsius

Celsius is a temperature scale most widely used around the world, especially in scientific work. Named after Swedish astronomer Anders Celsius, this scale fixes the freezing point of water at 0 degrees and the boiling point at 100 degrees.
This results in exactly 100 degrees between these two reference points.

• Freezing point of water: 0°C
• Boiling point of water: 100°C

Each degree on the Celsius scale represents the same amount of temperature change as a degree on the Kelvin scale. That's why they're sometimes mentioned together in scientific contexts. In terms of conversion, a 1-degree change in Celsius is equivalent to a 1.8-degree change in Fahrenheit. The straightforward, easy-to-understand increments make the Celsius scale simple and effective for everyday use and scientific calculations.

Kelvin

The Kelvin scale is the absolute temperature scale used in science and engineering. Unlike Fahrenheit and Celsius, Kelvin begins at absolute zero, the point where particles theoretically stop moving. The scale is named after Lord Kelvin.

• Absolute zero: 0 K
• Water's triple point: 273.15 K

In Kelvin, the freezing point of water is 273.15 K, and the boiling point is 373.15 K. Notably, a 1-degree change in Kelvin is equal to a 1-degree change in Celsius. Since both Celsius and Kelvin scales use the same size increment per degree, they make scientific calculations involving temperature easy and consistent. These features make the Kelvin scale invaluable for precise scientific measurements and research.