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I know that if it is 20deg C here in sunny Lincolnshire and only 10deg C in Shetland it is not twice as hot here as there, it's just that the number is twice as big.
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However, does the same hold true if we use Kelvin or does it actually work there? For example is something at 200deg K twice as hot as something at 100deg K, does it contain twice as much energy? Does the fact that Kelvin actually starts at zero make this work?
Yes, Kelvin is absolute.
For example is something at 200deg K twice as hot as something at 100deg K, does it contain twice as much energy?
Yes.
Does the fact that Kelvin actually starts at zero make this work?
Also yes. HTH.
For example is something at 200deg K twice as hot as something at 100deg K, does it contain twice as much energy?
Not necessarily iirc
FWIW; 10C is 283K, 20C is 293K so only 3.5% more.
It’s far more interesting (and real-world relevant be pending on how cold it gets where you live. Looking at you Canada) that -40C and -40F are the same.
Not necessarily iirc
I admit I assumed it was the same ‘something’, and I should add that I assumed no change of phase has occured between the temperatures! Also, it’s been a while since I made any thermo assumptions!
For example is something at 200deg K twice as hot as something at 100deg K, does it contain twice as much energy?
Yes, if its composition is identical. Specific heat capacity varies for different substances.
Kelvin needs some pants..
Doesn't state change absorb energy? IE if something is solid at 100k and liquid at 200k, changing state at 150k, the state change absorbs more energy?
Hmmm, If you're working in Celsius like the first example then no, I'd not considered it "twice as hot" it's ten degrees warmer, on that particular, commonly used scale. It's based around the state change of water (at sea level) innit; from a solid (ice) at 0*C to vapour (steam) at 100*c so a difference of 10*C = 10%.
I suppose Kelvin is the 'better' scale to use for a true scientific comparison in which case:
FWIW; 10C is 283K, 20C is 293K so only 3.5% more.
Edit: I edited my post above while shermer was making his post...
Interesting fact:
Anders Celsius actually proposed that degrees centigrade (as it was then known) ran in reverse- ie 0° is boiling and 100° is the freezing temp for water. It wasn't until after his death that Carl Linnaeus (as in the father of taxonomy) suggested that it might be better if the scale went the other way!
In the OP, we (as in people living in our climate who grew up with C) absolutely would say that if it was 20°C it was twice as hot as if it was 10°C. Starting at the triple point of water is a very useful reference point for weather, cooking etc… for most of what we do it is entirely irrelevant for us to compare to very low or very high temperatures. “What’s the temperate out there? It’s 4% warmer than yesterday” if it’s 10K warmer means nothing to us. It’s why we don’t use the scale starting at absolute zero in real life (rather than the lab). “Turn that oven up from 280K to 500K”… who’d say that at home? Where as “start with the oven at 220°C for 10 minutes to seal the meat, and then reduce it to half the temperature and leave it for 45 mins to slowly cook through” makes perfect sense to the home cook, who gives not one jot about what happens to their roast if their oven could operate at below -20°C.
As for liner relationship between temperature and energy, yes, for same material with no state changes, or chemical changes, or pressure changes, or… well, not really then.
Doesn’t state change absorb energy?
This.
Human feelings of being hot or cold aren't a scientific measurement scale in the way that temperature is. A 10 degree increase from 20 degrees C to 30 changes our feelings from comfortable to hot, going to 35 degrees is uncomfortably hot, after 40 degrees it becomes dangerously hot. It's not a linear thing.
Hotness is sum of random P.E and K.E of molecules. analogy is : Pizza base and cheese come out at 580K, both same temp, but cheese feels hotter when you bite in. Why?- cheese has changed state so without increase in K.E.( both base and cheese have same average random K.E) it has increased average random P.E. of molecules.
Without a change of state 200K is twice as hot as 100K. ( As previously posted)
But when you use your tongue / skin to quantify hotness - all values go out the window. Yes to "it's hotter" No to "it feels twice as hot"
cheese feels hotter when you bite in. Why?- cheese has changed state
I don't think this is true. Liquid cheese just transfers heat faster than pizza base, in the same way a block of iron passes heat faster than a stick, so feels colder to the touch if you pick one up outsidr
What on earth has change of state got to do with measured temperature. It changes the temperature profile of the matter as it is heated or cooled but if you measure it at any point that temperature is what it is and is exactly the same "hotness" as something kept at a stable temperature.
Or I've got physics wrong. Happy to be corrected.
What on earth has change of state got to do with measured temperature.
It's just the application, we're now used to a scale based on the state change of water to describe our environment (weather). It's not as 'precise' or absolute as K of course.
Admittedly it's generally towards the bottom end of that scale, but water's changes in state and human comfort/survivability do correlate quite well. Down around 0*C we won't last long without protection, and by the time you get us up to boiling we're pretty much done.
"Halfway" (50*C) is pushing things...
However, does the same hold true if we use Kelvin or does it actually work there? For example is something at 200deg K twice as hot as something at 100deg K
It's just Kelvin, not degrees Kelvin. It's a unit like a Kilogramme or a Volt.
What on earth has change of state got to do with measured temperature. It changes the temperature profile of the matter as it is heated or cooled but if you measure it at any point that temperature is what it is and is exactly the same “hotness” as something kept at a stable temperature.
The point is that measurable temperature does not have a linear relationship with energy. Like most of these things the confusion arises because commonly used terms (like 'hot') aren't actually very well defined.
Thermal energy is a useful term here, even though different flavours of scientists and engineers use it differently.
Thermal energy is often defined as the product of the Boltzmann constant and the absolute temperature (in Kelvin). This is related to the enthalpy of the system, which is a measure of heat and heat transfer. Heat transfer is what we feel, not temperature.
That said, and as others have pointed out, humans have a relatively narrow range of temperatures in which they can survive and one's experience of temperature in non-linear and depends on what you're used to.
In my experience, 20 oC is not/does not feel twice as hot as 10 oC.
What on earth has change of state got to do with measured temperature.
Same tempersature but more heat energy. Steam at 100 degrees will give you a nastier injury than water at 100 degrees.
I suppose if it's energy we want to be specific about should we find a different unit of measurement?
How about J/m^3 for whichever material you are looking at (air)?