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whoareyou
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Can someone explain the last paragraph of this slide? It doesn't make sense to me.
whoareyou said:Can someone explain the last paragraph of this slide? It doesn't make sense to me.
berkeman said:First, since it is addressing rates, the constants are no longer needed (does that make sense?).
Second, each of those fractions is equal to 1. Just like 1km/1000m = 1. You can use fractions like these to convert from one unit to another, or one rate to another involving the units.
So if you have a rate like 0.2mV per degree Celcius, you could convert that into a rate involving the Rankine temperature scale if that were of some help for some reason. Which one of those fractions would you use for such a conversion?
whoareyou said:I get how to do the converions, I just can't quite understand why when you want to convert to another temperature scale, you don't use the first set of equations listed. I mean 0°C != 1.8(32°F).
berkeman said:That's the rate issue that I mention in the first part of my post. If you differentiate an equation, what happens to the constants? The paragraph is discussing when you are dealing with rates that involve temperatures.
My example of 0.2mV per degree C is the temperature coefficient of voltage in a diode junction...
lurflurf said:So if we have a temperature difference we do not care about the values only the differences thus for differences
[tex]\Delta °R= \Delta °F[/tex]
[tex]\Delta °K= \Delta °C[/tex]
Thus we can use ratios like for absolute temperature
lurflurf said:K and °R are absolute temperature scales so conversion can be done by ratios. Absolute temperature can always be regarded as a change, that is absolute temperature=Absolute temperature-temperature absolute zero. °F and °C are not absolute so conversion requires also addition and subtraction. Temperature conversion in general can be effected by two reference temperatures say A and B
$$T^\prime =T_A ^\prime + \frac{T_B ^\prime-T_A ^\prime}{T_B -T_A }(T-T_A)$$
primes denote measurement in the new system
example
$$T_{human} (\,^{\circ}\mathrm{F}) =T_{water freeze} (\,^{\circ}\mathrm{F}) + \frac{T_{water boil} \,^{\circ}\mathrm{F}-T_{water freeze}\,^{\circ}\mathrm{F} }{T_{water boil}\,^{\circ}\mathrm{C} -T_{water freeze} \,^{\circ}\mathrm{C}}(T_{human}\,^{\circ}\mathrm{C}-T_{water freeze}\,^{\circ}\mathrm{C}) \\
=32\,^{\circ}\mathrm{F}+\frac{212\,^{\circ}\mathrm{F}-32\,^{\circ}\mathrm{F}}{100\,^{\circ}\mathrm{C}-0\,^{\circ}\mathrm{C}}(37\,^{\circ}\mathrm{C}-0\,^{\circ}\mathrm{C})=98.6\,^{\circ}\mathrm{F}$$
(that is just to illustrate conversion it is a common but questionable human temperature)
common reference temperatures include
absolute zero
freezing point water
triple point water
human body temperature
boiling point water
when we work in absolute temperature we have absolute zero=0
so
$$T^\prime =T_A ^\prime + \frac{T_B ^\prime-T_A ^\prime}{T_B -T_A }(T-T_A)$$
becomes
$$T^\prime =0 + \frac{T_B ^\prime-0}{T_B -0 }(T-0)=\frac{T_B ^\prime}{T_B }T$$
To convert Fahrenheit to Celsius, use the formula (°F - 32) x 5/9 = °C. Subtract 32 from the temperature in Fahrenheit, then multiply that number by 5/9 to get the temperature in Celsius.
The formula for converting Celsius to Fahrenheit is (°C x 9/5) + 32 = °F. Multiply the temperature in Celsius by 9/5, then add 32 to get the temperature in Fahrenheit.
To convert Kelvin to Celsius, simply subtract 273.15 from the temperature in Kelvin. This will give you the temperature in Celsius.
Fahrenheit and Celsius are two different temperature scales used to measure temperature. The Fahrenheit scale is primarily used in the United States, while the Celsius scale is used in most other countries. The freezing point of water on the Fahrenheit scale is 32°F, while on the Celsius scale it is 0°C. The boiling point of water on the Fahrenheit scale is 212°F, while on the Celsius scale it is 100°C.
Yes, there are many online calculators available that can quickly and accurately convert between different temperature scales. Simply enter the temperature you want to convert and select the desired scale to get the conversion result.