Twice The Temperature

[kennythebomb]

Is it scientifically correct to say "Chicago is twice as warm as Detroit" if Chicago is at 80 degrees and Detroit 40?

Granted, I'm using the fahrenheit scale, and even if I was using centigrade 'twice as much' degree does not equal twice as much perceived warmth, I would assume.

Also, it would seem to me that finding a way to measure perceived warmth on an actual relative scale would be impossible due to the sheer amount of solar energy that we call heat. Unless I am mistaken on the terminology or method here.

Obviously there is no discernible change from 1 degrees to 2 degrees, but you hear people say 'it is twice as warm today'.

So is there an actual, exact way to measure perceived warmth.. and then is there a temperature scale that is built off of that?

 

[Keef]

I don't see how that could be scientifically correct. Absolute Zero (as we know it) is something like -470 degrees fahrenheit. So, if Chicago was -400 while Detroit was -435, then it would be twice as warm.

But I don't know if "warm" is eve the right word for te scenario. It'd have twice the heat energy, at least.

And I believe the Kelvin scale begins at Absolute Zero, and goes up from there.

 

[Philly]

I'll agree here. Based on Kelvin, starting at absolute zero, chicago wouldn't be much warmer than detroit. (relative) Of course, that would mean chicago has twice as much energy in its air than Detroit. On the farenheit scale, for something to be twice as warm as 40º, I would guess 48 because 40 is equidistant from freezing and 48, assuming that zero has no real meaning on the Farenheit scale. In celsius, I would say 40 is half as warm as 80, but that's pretty hot.

So, my question, what does zero mean on the farenheit scale?

 

[Keef]

Excuse me, Absolute Zero is -459.67 degrees Fahrenheit.

As for Fahrenheit's zero, read this, beginning in the "history" section...

http://en.wikipedia.org/wiki/Fahrenheit

 

[wfooshee]

Chicago at 80 would be twice as far from the freezing point of salt water as Detroit at 40. That's about it.

As for something being "twice as warm," the only scale I would think of that actually shows that would be Kelvin, starting with absolute zero.

 

[kennythebomb]

Chicago at 80 would be twice as far from the freezing point of salt water as Detroit at 40. That's about it.

As for something being "twice as warm," the only scale I would think of that actually shows that would be Kelvin, starting with absolute zero.

If that is true, than we will never experience temperatures in our regular lives that can be 'twice as' something else, using the Kelvin scale as a means for measuring perceived warmth.

 

[Sureboss]

Unless you're under a nuclear bomb...

 

[Famine]

If you're using (any scale here) to measure temperature and one place is at 40 and another is at 80 then yes, 80 is twice as hot as 40.

If you want to convert temperature into thermal energy then it isn't, but so long as you're using an arbitrary scale for temperature then 2n is twice as hot as n.

 

[Danoff]

It doesn't make sense to use Fahrenheit or Celsius to make an evaluation of a concept like "twice the heat". Use an absolute scale like Kelvin or Rankine. Celsius is a measurement with respect to the freezing point of water. So if you want to measure "twice the distance from freezing" you'd want to use that. I don't know what you'd want to use Fahrenheit for...

 

[Famine]

Brits use Celsius for cold and Farenheit for hot.

"Cripes, it's 90 out today!"
"Blimey, it was -4 last night!"

 

[Danoff]

Brits use Celsius for cold and Farenheit for hot.

"Cripes, it's 90 out today!"
"Blimey, it was -4 last night!"

 

[kennythebomb]

Brits use Celsius for cold and Farenheit for hot.

"Cripes, it's 90 out today!"
"Blimey, it was -4 last night!"

Well hell those could both be fahrenheit, unless you are meaning both in the same day, in which that would be a strange day!

Thanks for the answers guys.

 

[Philly]

Excuse me, Absolute Zero is -459.67 degrees Fahrenheit.

As for Fahrenheit's zero, read this, beginning in the "history" section...

http://en.wikipedia.org/wiki/Fahrenheit

I thought about 0 being the freezing temperature of salt water, but doesn't that freeze around 19ºF?

I guess Famine's answer to the question does make sense. 12 cm. is twice as close as 6cm. 18 in. is half as far as 36 in.

 

[Boundary Layer]

If you're using (any scale here) to measure temperature and one place is at 40 and another is at 80 then yes, 80 is twice as hot as 40.

If strictly comparing two temperatures, I think it is correct to say that 20*C is twice the temperature of 10*C, etc, even if not true when converted to a different system of measure. You can not, however, say that 20*C is twice as hot as 10*C because now you are no longer talking about temperature, you're talking about heat.

To the touch, 2*C does not feel 2x hotter than 1*C, just as 1*C does not feel inifinitely hotter than 0*C. We do not feel temperature, we feel thermal energy being added or extracted from our bodies. A common 6th grade science experiment verifies this - take 3 buckets of water, 1 filled with hot water, 1 filled with chilled water, and 1 with room temperature water... I'm sure you know the rest.
Temperature scales were only developed for convenience and are based on the behaviour of different materials as energy is added or extracted from them. The Celsius scale was developed around water freezing and boiling in atmospheric conditions, Farenheit developed his scale around ice melting in a salt solution and the temperature of his wife's armpits.


For ideal gases (air is one), using the Kelvin scale is a decent way to compare the heat between two bodies if you want to describe one as being a multiple of the other - it's not exact, but close enough.

What I think you really want to do is compare the enthalpy (h) of a unit volume at pt. A to the enthalpy of a unit volume at pt. B. Enthalpy is a fancy word meaning 'total heat' (or u+Pv). For air, or any other ideal gas I have a table for in my thermo text, the enthalpy varies at an approximately linear rate as temperature increases.

For example, air at 295K (room temperature) has an enthalpy of 295.17 [kJ/kg]. At 590K air has an enthalpy of 596.52 [kJ/kg].
596.52/295.17 = 2.02094

Enthalpy of hydrogen (H2) at 300K is 8522 [kJ/kmol], at 600K, 17280 [kJ/kmol]
17280/8522=2.02769

This only works on ideal gases though because their specific heats are only functions of temperature. T[K] can not be used to compare heat on solids & liquids whose specific heats are functions of temperature and internal energy (u), or a material that undergoes (or is undergoing) a phase change between two temperatures because the phase change requires additional input of energy, (like water/steam). Saturated water at 100*C and 101.35 [kPa] has an enthalpy of 419.04 [kJ/kg], saturated water vapor at the same temperature and pressure has an enthalpy of 2676.1 [kJ/kg].

 

[Sureboss]

I don't think it is correct to say that 40 is twice as hot as 20. Because the scale doesn't start at 0 does it?

 

[kennythebomb]

Thank you boundary, I understand the concept a lot better now.

 

[Kylehnat]

If you're using (any scale here) to measure temperature and one place is at 40 and another is at 80 then yes, 80 is twice as hot as 40.

But the temperature scale you're using can't have negative value. If it's 50 degrees in City A and -5 degrees in City B, it doesn't make sense to say that the temperature in City A is -10 times that of the temperature in City B.

If today, the temperature was 40 degrees, and yesterday, the temperature was zero degrees, is today infinitely hotter than yesterday? If today was 1 degree, is it still infinitely hotter than yesterday? Or did I just blow your mind?

Furthermore, the concept of "hot" and "cold" is subjective. Humans have a very narrow range of comfort. In an absolute scale (Kelvin), the comfort range is about 290-300 degrees. Let's call "hot" 315 Kelvin, and "cold" 270 Kelvin. In terms of thermal energy, "hot" is only about 15% "hotter" than "cold".

This is too much thinking. I'm going to bed.

 

[Boundary Layer]

But the temperature scale you're using can't have negative value. If it's 50 degrees in City A and -5 degrees in City B, it doesn't make sense to say that the temperature in City A is -10 times that of the temperature in City B.

Good point.

If today was 1 degree, is it still infinitely hotter than yesterday? Or did I just blow your mind?

Pretty sure you didn't, since I raised the same issue 2 days ago.

Let's call "hot" 315 Kelvin, and "cold" 270 Kelvin. In terms of thermal energy, "hot" is only about 15% "hotter" than "cold".

No, what you described is in terms of absolute temperature, not thermal energy. You should have said "In terms of absolute temperature, hot is only about 15% hotter than cold". You haven't specified a material.

If it's water at 273.15K and 313.15K at atmospheric pressure the two enthalpies are 0.01 [kJ/kg] and 167.57 [kJ/kg] respectively. The difference in that case is much much more than 15%.

Or, maybe you meant that the human body surface temperature is at 270K or 315K. The human body has a specific heat of approximately 3.47 [(kJ/kg)K] (but varies slightly with temperature), meaning that it requires 3.47 kJ of heat per kg of human tissue to raise the temperature of that tissue by 1K. For comparison, the specific heat of air is roughly 1 [kJ/kg)k] (but it also varies slightly with temperature).

I have not bothered to calculate the %-change in thermal energy of human flesh at the 'hot' and 'cold' points you specified because I don't know the internal energy of human tissue at 270K (it's a tough number to find without causing severe cell damage or death). But my point is that it is incorrect to generalize and say that for all substances there is a xx% change in thermal energy between temp A and B.

 

[Danoff]

For example, air at 295K (room temperature) has an enthalpy of 295.17 [kJ/kg]. At 590K air has an enthalpy of 596.52 [kJ/kg].
596.52/295.17 = 2.02094

Enthalpy of hydrogen (H2) at 300K is 8522 [kJ/kmol], at 600K, 17280 [kJ/kmol]
17280/8522=2.02769

In both of those examles, the temperature change alone provided an excellent measure of the difference:
590K/295K=2.0
600K/300K=2.0

 

[Boundary Layer]

^yup, that was mentioned.

For ideal gases (air is one), using the Kelvin scale is a decent way to compare the heat between two bodies if you want to describe one as being a multiple of the other - it's not exact, but close enough.

....

This only works on ideal gases though because their specific heats are only functions of temperature.

 

[Danoff]

^yup, that was mentioned.

I guess I should read more carefully.

So on a side note, you seem to know a thing or two about Thermodynamics. What do you do for a living? I'm guessing it has something to do with turbulent boundary layers. I'd have guessed that you do something with drag, but now I'm starting to think that you're a heat transfer kind of guy. To totally go FTW, does this look familiar?

 

[kennythebomb]

Are there partial derivs in there?

 

[Danoff]

Are there partial derivs in there?

Yup. In college I had to memorize that equation (among others from the suite).

 

[Boundary Layer]

@Danoff:
I'm a mechanical engineering student, so right now I do everything and get paid for none of it.

And that's the general Navier-Stokes equation. What a nightmare. Gotta admit, I don't have that one memorized, I've only memorized it for the specialized case of incompressible flow and constant viscosity.

Oh, and there's boundary layers in heat transfer and fluids. Very closely tied.

 

[Danoff]

And that's the general Navier-Stokes equation. What a nightmare.

I still have nightmares about it occasionally, those equations scarred me for life.

Oh, and there's boundary layers in heat transfer and fluids. Very closely tied.

Yup... and I don't like either one.

 

[Omnis]

But the temperature scale you're using can't have negative value. If it's 50 degrees in City A and -5 degrees in City B, it doesn't make sense to say that the temperature in City A is -10 times that of the temperature in City B.

But if we're talking about absolute values here, it makes perfect sense to say that -5 is ten times colder than 50.

 

[Danoff]

But if we're talking about absolute values here, it makes perfect sense to say that -5 is ten times colder than 50.

Not following... -5 and 50 are 55 degrees apart.

 

[Omnis]

Not following... -5 and 50 are 55 degrees apart.

HAHAHAHAHA! Sorry, idiot moment.


(11 times... )

 

[Danoff]

HAHAHAHAHA! Sorry, idiot moment.


(11 times... )

No problem.

I would say that the difference is 1100% of the value - or that the difference is 11 times the value (in degrees Celsius). I don't think I'd say that one temp is 11 times the other temp when they cross zero. Because -5 is only 45 degrees closer to zero than 50 degrees is.

 

[Kylehnat]

You should have said "In terms of absolute temperature, hot is only about 15% hotter than cold". You haven't specified a material.

When speaking of ambient temperature, the only material is air.

If it's water at 273.15K and 313.15K at atmospheric pressure the two enthalpies are 0.01 [kJ/kg] and 167.57 [kJ/kg] respectively. The difference in that case is much much more than 15%.

That's because you picked an arbitrary substance, which just happens to freeze at 273 K. The case would be quite different if you picked mercury, antifreeze, or vodka.

In any case the only substance that matters here is air--a close-to-ideal gas.

Or, maybe you meant that the human body surface temperature is at 270K or 315K. The human body has a specific heat of approximately 3.47 [(kJ/kg)K] (but varies slightly with temperature), meaning that it requires 3.47 kJ of heat per kg of human tissue to raise the temperature of that tissue by 1K. For comparison, the specific heat of air is roughly 1 [kJ/kg)k] (but it also varies slightly with temperature).

Having fun going through Appendix A of your heat transfer book?

Boundary Layer]But my point is that it is incorrect to generalize and say that for all substances there is a xx% change in thermal energy between temp A and B.

You're right: we can't generalize xx% change for every material known to man, but we're not. We're comparing air at different temperatures.

Oh, and there's boundary layers in heat transfer and fluids. Very closely tied.

There are also boundary layers in mass transfer, the 800-pound gorilla of transport phenomena. Mass transfer is by far the best of the three (though confusing; diffusive flux imparts bulk velocity? Huh?). However, fluid mechanics and heat transfer have a greater number of practical applications (unless your business is building gas-stripping towers).

[ugly equation]

If you ever bring the Navier-Stokes equation back to GTP, I will be forced to hunt you down and tattoo it on your genitals.