degrees Rankine (R) to Kelvins (K) conversion

What is degrees rankine?

Degrees Rankine ($^\circ R$) is a thermodynamic (absolute) temperature scale named after the Scottish physicist and engineer William John Macquorn Rankine, who proposed it in 1859. It's primarily used in engineering, particularly in the United States. Let's delve into its details.

Definition and Origin

The Rankine scale, like the Kelvin scale, is an absolute temperature scale, meaning its zero point (0 $^\circ R$) corresponds to absolute zero, the theoretical temperature at which all molecular motion ceases. The key difference is that the Rankine scale uses the Fahrenheit degree as its unit interval, whereas the Kelvin scale uses the Celsius degree.

Conversion Formulas

Here's how to convert between Rankine and other common temperature scales:

• Rankine to Fahrenheit:

  $^\circ R = ^\circ F + 459.67$

• Rankine to Celsius:

  $^\circ R = (^ \circ C + 273.15) \times \frac{9}{5}$

• Rankine to Kelvin:

  $^\circ R = K \times \frac{9}{5}$

The zero point of the Rankine scale is absolute zero, which is −459.67 $^\circ F$ or -273.15 $^\circ C$.

Historical Context and William Rankine

William John Macquorn Rankine (1820-1872) was a prominent Scottish engineer and physicist. He made significant contributions to thermodynamics, engine design, and soil mechanics. The Rankine cycle, a fundamental concept in thermodynamics describing the operation of heat engines, is also named after him. While he is known for the Rankine scale, his broader work in thermodynamics had a more lasting impact. He was the first to use the term "Thermodynamics"

Practical Applications and Examples

While not as widely used as Celsius, Fahrenheit, or Kelvin, the Rankine scale finds applications in specific engineering contexts, particularly in the United States, especially when dealing with thermodynamic calculations.

• Thermodynamics: In engineering thermodynamics, the Rankine scale is valuable when absolute temperature values are needed, simplifying calculations involving energy transfer and thermodynamic processes.
• Combustion: When analyzing combustion processes, using absolute temperature scales like Rankine avoids potential issues with negative temperature values in calculations.
• Aviation: Although less common now, some older engineering practices in aviation might have utilized Rankine for certain calculations related to engine performance or atmospheric conditions.

Examples of approximate Rankine values for common temperatures:

• Freezing point of water: 491.67 $^\circ R$
• Boiling point of water: 671.67 $^\circ R$
• Standard room temperature (25 $^\circ C$ or 77 $^\circ F$): 536.67 $^\circ R$

Advantages and Disadvantages

Advantages:

• It is an absolute temperature scale, which is useful in thermodynamic calculations.
• It uses the Fahrenheit degree, which is familiar to engineers in the United States.

Disadvantages:

• It is not as widely used as Celsius, Fahrenheit, or Kelvin.
• The Fahrenheit degree is smaller than the Celsius degree, which can make calculations more difficult.

Further Reading

For a deeper understanding, consider exploring these resources:

• Thermodynamic temperature - Wikipedia

What is Kelvins?

Kelvin is the base unit of temperature in the International System of Units (SI), commonly used in scientific and engineering fields. It's an absolute thermodynamic temperature scale, meaning its zero point is absolute zero, the point at which all molecular motion ceases.

Definition of Kelvin

The Kelvin scale is defined by setting the triple point of water (the temperature at which water can exist in equilibrium as a solid, liquid, and gas) to exactly 273.16 K. A temperature difference of 1 Kelvin is the same as a temperature difference of 1 degree Celsius. The symbol for Kelvin is K (no degree symbol).

The Formation of the Kelvin Scale and Lord Kelvin

The Kelvin scale is named after William Thomson, 1st Baron Kelvin (1824–1907), a British physicist who proposed the absolute thermodynamic temperature scale. He recognized the need for a temperature scale with an absolute zero point, independent of the properties of any particular substance. The concept of absolute zero arises from extrapolating the behavior of gases as they cool.

Lord Kelvin contributed significantly to thermodynamics, electromagnetism, and other areas of physics. He formulated the second law of thermodynamics and played a key role in the development of the transatlantic telegraph cable.

Converting to and from Kelvin

Here are the formulas to convert between Kelvin and other common temperature scales:

• Celsius to Kelvin: $K =$^\circ C + 273.15$
• Fahrenheit to Kelvin: $K = (^\circ F - 32) \times \frac{5}{9} + 273.15$

Interesting Facts About Kelvin

• Absolute Zero: Absolute zero (0 K or -273.15 °C) is theoretically the lowest possible temperature. In practice, it's impossible to reach absolute zero perfectly, although scientists have come incredibly close.
• No Negative Values: Unlike Celsius or Fahrenheit, the Kelvin scale does not have negative values. This is because it starts at absolute zero, the lowest possible temperature.

Real-World Examples of Kelvin Temperatures

• Space: The average temperature of the cosmic microwave background radiation (the afterglow of the Big Bang) is about 2.7 K.

• Cryogenics: Liquid helium, used in cryogenics for cooling superconducting magnets in MRI machines, has a boiling point of approximately 4.2 K.

• Light Bulbs: The surface of the sun is about 5,778K. Standard incandescent light bulbs operate at temperatures of 2,500-3,000 K. This can be measured using principles of blackbody radiation and Wien's displacement law to see how the peak wavelength is inversely proportional to temperature:

  $\lambda_{max} = \frac{b}{T}$

  where $b$ is Wien's displacement constant ($2.898 \times 10^{-3} m \cdot K$) and $T$ is the temperature in Kelvin.

• Material Science: The melting point of various materials is often expressed in Kelvin. For example, the melting point of copper is 1357.77 K.

• Scientific Research: Kelvin is extensively used in scientific research, especially in fields like physics, chemistry, and materials science, where precise temperature measurements are essential.