The term Rankine refers to two distinct and significant concepts within the fields of thermodynamics and engineering, both named after the 19th-century Scottish polymath William John Macquorn Rankine. These concepts are the Rankine temperature scale and the Rankine power generation cycle, which serve entirely different purposes. The temperature scale is a scientific tool for absolute measurement. In contrast, the power cycle is a model describing the operation of steam engines and power plants used to generate power. Understanding the connection to its namesake provides a foundation for exploring these two separate but influential concepts.
The Absolute Temperature Scale
The Rankine scale (°R or °Ra) is a thermodynamic temperature scale whose zero point is set at absolute zero (0 °R), the theoretical temperature where all particle motion ceases. This absolute nature is significant because scientific calculations involving gas laws and thermodynamic equations require a scale that begins at true zero. Without this feature, the mathematical relationships between temperature, pressure, and volume would not hold true.
The Rankine scale serves as the absolute counterpart to the Fahrenheit scale, much like the Kelvin scale is the absolute counterpart to the Celsius scale. The foundational principle is that a temperature difference of one degree Rankine is exactly equal to a temperature difference of one degree Fahrenheit. This defining characteristic makes it useful in engineering applications, especially in the United States, where the Fahrenheit scale is still prevalent. By adopting the same degree size, engineers working with the Fahrenheit system can easily transition to an absolute scale for complex thermodynamic calculations.
Setting absolute zero at 0 °R places it at -459.67 °F on the conventional Fahrenheit scale. Any temperature measured in Fahrenheit can be converted to Rankine simply by adding 459.67 to the Fahrenheit value. For instance, the freezing point of water, 32 °F, is 491.67 °R. Although less common globally than the Kelvin scale, the Rankine scale remains a precise method for dealing with extreme temperatures in specific industrial and scientific contexts.
Converting Between Temperature Systems
Converting a temperature from the Rankine scale to other common systems involves specific mathematical relationships that reflect the difference in their starting points and degree sizes. The most straightforward conversion is to the Fahrenheit scale, which shares the same degree interval as Rankine. To find the Fahrenheit temperature (°F), one simply subtracts 459.67 from the Rankine temperature (°R). For example, a steam temperature of 1000 °R is equal to 540.33 °F.
The conversions to the metric-based scales, Kelvin (K) and Celsius (°C), require accounting for the difference in degree size. A Rankine degree is 5/9 the size of a Kelvin or Celsius degree. To convert Rankine to Kelvin, the Rankine temperature must be divided by the ratio of 1.8. Therefore, if a gas is measured at 800 °R, the temperature in Kelvin is approximately 444.44 K.
Converting from Rankine to Celsius involves a two-step process: first converting to Kelvin and then subtracting the fixed difference between Kelvin and Celsius. Since the Kelvin and Celsius scales are offset by 273.15, the formula is °C = (°R / 1.8) – 273.15. For instance, a comfortable room temperature of 530 °R converts to 21.29 °C. These specific formulas allow for accurate translation of absolute temperature values across the different measurement systems used worldwide.
The Rankine Power Generation Cycle
The Rankine cycle is a thermodynamic model describing how heat energy is converted into mechanical work, primarily in steam-based power generation plants. It is the fundamental operating process for nearly all thermal power stations, including those powered by coal, nuclear fission, natural gas, and concentrated solar energy. Its purpose is to efficiently harness thermal energy from a heat source to generate electricity by continuously circulating a working fluid, typically water, through four main components in a closed loop.
The Pump
The first stage is the pump, which takes low-pressure liquid water from the condenser and compresses it to a high-pressure liquid. This compression requires work input and prepares the fluid for the next stage.
The Boiler
The second stage is the boiler, where heat is added to the high-pressure liquid, converting it into high-pressure steam at a constant pressure. This transformation transfers energy from the fuel source into the working fluid.
The Turbine
In the third stage, the high-pressure steam is directed into a turbine, where it expands and pushes against the blades. This expansion converts the thermal energy of the steam into rotational mechanical energy, which drives an electrical generator.
The Condenser
Finally, the low-pressure steam exiting the turbine enters the condenser. Here, the steam is cooled and rejects waste heat to an external heat sink, causing it to condense back into a saturated liquid. This condensation step significantly lowers the pressure at the turbine outlet, minimizing the work required by the pump.