Question

Which unit is the smallest: one Celsius degree, one kelvin, or one Fahrenheit degree? Explain your thinking.

Short answer

The smallest unit is one Fahrenheit degree.

Step-by-step solution

Introduction to Temperature Units

To determine which unit is the smallest, it's important to first understand each unit's scale and relationship: Celsius and Kelvin have the same magnitude (1 degree change in Celsius equals 1 degree change in Kelvin), while the Fahrenheit scale is different.

Unit Conversion Relations

The relationship between these units can be described by conversion formulas:1. Celsius to Kelvin: \[ K = °C + 273.15 \] This indicates that a degree change in Celsius is equivalent to a degree change in Kelvin since the conversion is just a shift.2. Celsius to Fahrenheit: \[ °F = \left( °C \times \frac{9}{5} \right) + 32 \] From this, a 1 degree change in Celsius results in a 1.8 degree change in Fahrenheit.

Comparison of Temperature Unit Magnitudes

Given the conversion relationship, 1 degree Kelvin is equivalent to 1 degree Celsius and both are larger than 1 degree Fahrenheit. This is due to the factor of \( \frac{9}{5} = 1.8 \) between Celsius and Fahrenheit.

Conclusion

Since 1 degree change in Celsius (or Kelvin) results in a 1.8 degree change in Fahrenheit, the Fahrenheit unit is smaller. Therefore, 1 degree Fahrenheit is the smallest unit of temperature change among the three.

Key concepts

Celsius

The Celsius scale, also known as the centigrade scale, is a temperature measurement system commonly used worldwide, especially where the metric system prevails. Named after the Swedish astronomer Anders Celsius, this scale is based on the freezing and boiling points of water. The defining points are 0°C, which is the freezing point of water, and 100°C, the boiling point of water at standard atmospheric pressure.

The Celsius scale is highly intuitive since it divides the temperature range between the freezing and boiling points of water into 100 equal parts. This makes it a practical choice for many scientific and everyday applications. One degree Celsius change reflects the same magnitude as a one Kelvin change, which we'll explore further in our next section.

Kelvin

The Kelvin scale is the absolute temperature scale used mostly in scientific contexts. Unlike the Celsius scale, the Kelvin scale starts at absolute zero, the theoretical point where no thermal energy remains in a substance. Absolute zero is 0 K, which is equivalent to -273.15°C.

A simple addition of 273.15 to a Celsius temperature can translate it into Kelvin: \( K = °C + 273.15 \).

The Kelvin scale does not use the degree symbol; temperatures are articulated simply as 'kelvins.' Its use in science stems from its absolute nature and consistency, making it crucial for thermodynamic studies and energy-related calculations.

Fahrenheit

The Fahrenheit scale is used primarily in the United States and a few other countries for everyday temperature measurement. This scale was named after German physicist Daniel Gabriel Fahrenheit. In the Fahrenheit system, the freezing point of water is 32°F and the boiling point is 212°F at standard atmospheric pressure.

The scale divides the freezing and boiling intervals of water into 180 equal parts, leading to a conversion formula from Celsius: \( °F = \left( °C \times \frac{9}{5} \right) + 32 \).

This means that a one-degree change on the Celsius scale equals a 1.8-degree change on the Fahrenheit scale, making the Fahrenheit degree intervals smaller. This is why, when comparing temperature changes, the unit in Fahrenheit is the smallest among Celsius, Kelvin, and Fahrenheit.

Unit Conversion

Unit conversion between temperature scales is essential for scientific consistency and everyday practicality. Converting between Celsius, Kelvin, and Fahrenheit involves straightforward mathematical relationships:

• Celsius to Kelvin: \( K = °C + 273.15 \)
• Celsius to Fahrenheit: \( °F = \left( °C \times \frac{9}{5} \right) + 32 \)
• Fahrenheit to Celsius: \( °C = \frac{5}{9}(°F - 32) \)

Understanding these formulas can help in converting temperatures for various applications, whether cooking, weather reporting, or scientific experiments. Learning these conversions ensures clear communication and effective problem-solving across different regions and contexts.

Temperature Scales

Temperature scales are systems used to quantify the sensation of hot and cold. The three most commonly used scales are Celsius, Kelvin, and Fahrenheit. Each scale has its specific use but they all essentially measure the same physical property: temperature.

• The Celsius scale aligns closely with everyday life, especially in regions that use the metric system.
• The Kelvin scale is critical in scientific research due to its absolute scale starting from zero kelvin.
• The Fahrenheit scale is prevalent in the United States for meteorological, heating, cooling, and cooking purposes.

All of these scales have unique historical and practical backgrounds, but they serve the universal goal of temperature measurement, enabling us to understand and express thermal energy in different contexts.