33 Temperature Conversions
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So what is temperature and how is it different from heat?
Temperature is the average kinetic energy of particles. An object’s temperature is an indication of the amount of thermal energy present in the object. There are four units of measure for temperature; Fahrenheit, Celsius, Rankine, and Kelvin. Most people are familiar with the freezing and boiling point of water, 32°F/0°C and 212°F/100°C respectively. Another reference point known as Absolute Zero, is a theoretical point where all particles stop moving. Absolute zero occurs at 0 Rankine, 0 Kelvin, −273.15 Celsius, and −459.67 Fahrenheit.
Heat is the transfer of thermal energy. Thermal energy transfer can occur through conduction, convection, and radiation. The most common unit of measure for Heat is the British Thermal Unit (BTU) which represents the amount of thermal energy required to increase one pound of water one degree Fahrenheit.
Introduction to Thermodynamics
Lessons in Industrial Instrumentation: Chapter 2: Section 10: Page 120-129 (pdf pg 145- 154)
Temperature unit conversion can be a simple process if the relationship between the units is understood. Given the fact that water freezes at 273.15 K = 0°C = 32°F = 491.67°R and boils at 373.15 K = 100°C = 212°F = 671.67°R, we can determine a ratio relationship between the units. The rate of change for each unit from freezing to boiling is 100 K, 100°C, 180°F and 180°R. These rates of change can be simplified to:
- 1 K : 1°C
- 1°R : 1°F
- 1°C : 1.8°F
- 1 K : 1.8°R
At Absolute Zero, the Rankine and Kelvin scale start at zero. As demonstrated above, there is a 1.8°R : 1 K ratio. Since both units start at zero at Absolute Zero the only the ratio needs to be applied during the conversion between these units. For example, if you are asked to convert 365K to Rankine, you simply multiply 365K by 1.8°R /1 K = 657°R.
As indicated above, the Kelvin and Celsius units have a 1:1 ratio. What this means is that for every 1 degree change in Kelvin, there is a one degree change in Celsius. However, these units don’t start at the same zero, so a correction must be made. There is a 273.15 degree difference that must be applied. When converting Kelvin to Celsius subtract 273.15. When converting from Celsius to Kelvin add 273.15.
Rankine and Fahrenheit also have a 1:1 ratio. However, these units do not have the same zero and require a 459.67 degree correction. When converting Rankine to Fahrenheit subtract 459.67. When converting from Fahrenheit to Rankine add 459.67.
Celsius and Fahrenheit conversions can be difficult because they require a non-zero correction and ratio application. Referencing the freezing point of water, we see there is a 32 degree difference between Fahrenheit and Celsius. As demonstrated above, there is a 1°C : 1.8°F ratio. When converting, the zero point and ratio must be applied. For example, converting 100°F to Celsius would require the following mathematical operation:
(100°F-32°F)/(1.8°F/1°C) = 37.78°C
Or if converting 125°C to Fahrenheit the following mathematical operation would be performed:
(125°C*(1.8°F/1°C))+32°F = 257°F
Conversion factors for temperature
Lessons in Industrial Instrumentation: Chapter 2: Section 4: Page 64 (pdf pg 89)
Now that temperature scale conversions have been covered, let’s examine the rate of change. It is important to understand how and when to apply scale conversions versus rate of change ratio conversions. For example:
A process fluid inlet temperature is 60°F. The heat exchanger is increasing a process fluid’s temperature by 10°C. What is the outlet temperature in Fahrenheit?
By examining this example, we see that the inlet temperature (60°F) is a scale value. The increase in temperature (10°C) is a rate of change. The problem can be solved two ways: 1) Convert 60°F into Celsius, adding the 10°C, then converting back to Fahrenheit; OR 2) We know the ratio is 1.8°F : 1 °C, so a rate of change of 10°C is the same as a 18°F, mathematically this second approach is a much simpler way to solve since we apply the ratio and then add the 18°F to 60°F for a final temp of 78°F.