Like the Kelvin scale, the Rankine scale is an absolute temperature scale: Absolute zero is zero degrees Rankine (0°R). However, the units of this scale are the same size as those of the Fahrenheit scale rather than the Celsius scale. What is the numerical value of the triple-point temperature of water on the Rankine scale?

Verified step by step guidance

1. Understand the concept of the triple-point temperature of water, which is the temperature at which water can coexist in equilibrium in its solid, liquid, and gaseous states. This temperature is 0.01°C on the Celsius scale and 273.16 K on the Kelvin scale.
2. Recognize that the Rankine scale is an absolute temperature scale similar to the Kelvin scale, but it uses Fahrenheit-sized degrees. Therefore, the conversion between Kelvin and Rankine involves multiplying the Kelvin temperature by a factor to account for the difference in degree size.
3. Recall the conversion formula between Kelvin and Rankine: \( T_R = T_K \times \frac{9}{5} \), where \( T_R \) is the temperature in Rankine and \( T_K \) is the temperature in Kelvin.
4. Apply the conversion formula to the triple-point temperature of water: \( T_R = 273.16 \times \frac{9}{5} \). This will give you the temperature in degrees Rankine.
5. Perform the multiplication to find the numerical value of the triple-point temperature of water on the Rankine scale, ensuring that you maintain the precision of the calculation.

Key Concepts

Absolute Temperature Scale

An absolute temperature scale is one where the zero point is absolute zero, the theoretical temperature at which particles have minimal thermal motion. The Kelvin and Rankine scales are examples, with Kelvin using Celsius-sized units and Rankine using Fahrenheit-sized units. Absolute scales are crucial for thermodynamic calculations.

Triple Point of Water

The triple point of water is the unique temperature and pressure at which water can coexist in equilibrium in its solid, liquid, and gaseous states. It is precisely defined as 273.16 Kelvin, which serves as a reference point for temperature scales. Understanding this concept is essential for converting temperatures between different scales.

Temperature Conversion

Temperature conversion involves translating a temperature from one scale to another. For the Rankine scale, which uses Fahrenheit-sized units, the conversion from Kelvin involves multiplying by 1.8 (since 1 Kelvin equals 1.8 Rankine). This conversion is necessary to find the triple-point temperature of water in Rankine, which is 491.67°R.