Using the freezing and boiling point temperatures for water...

Name: Problem 94, Chapter 1: Fundamentals of Thermodynamics
Uploaded: 2020-07-25T11:14:02-08:00
Duration: 2 min 38 s
Channel: Sophie S
Description: Using the freezing and boiling point temperatures for water on both the Celsius and Fahrenheit scales, develop a conversion formula between the scales. Find the conversion formula between the Kelvin and Rankine temperature scales.

Using the freezing and boiling point temperatures for water on both the Celsius and Fahrenheit scales, develop a conversion formula between the scales. Find the conversion formula between the Kelvin and Rankine temperature scales.

Key Concepts

Linear Transformation in Temperature Conversions

Temperature conversion formulas are based on linear transformations, where one temperature scale is converted to another using a formula of the form y = mx + b. This approach leverages the fact that most temperature scales are linearly related, meaning that equal intervals on one scale correspond to equal intervals on the other, with the addition of a fixed offset between their starting points.

Using Fixed Reference Points

Fixed reference points, such as the freezing and boiling points of water, are essential for defining temperature scales. These points are used to establish the scaling and offset parameters in the conversion formulas. By knowing the values of these benchmarks on two different scales, one can derive the linear transformation that accurately converts temperatures between the scales.

Celsius-Fahrenheit Conversion Formula

The conversion between Celsius and Fahrenheit is derived using the defined fixed points of water. The formula F = (9/5) * C + 32 is established by aligning the freezing point of water at 0°C (32°F) and the boiling point at 100°C (212°F). This conversion is an application of the linear transformation concept where the slope (9/5) and the intercept (32) are determined by the difference in the fixed reference points.

Kelvin-Rankine Conversion

Kelvin and Rankine are both absolute temperature scales, meaning they start from absolute zero, the theoretical lowest possible temperature. The conversion formula between Kelvin and Rankine, given by R = (9/5) * K, is a straightforward linear relationship derived from the proportionality of their unit increments. Since there is no offset between the scales, only a scaling factor, the conversion is simpler compared to converting Celsius to Fahrenheit.

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