Is 10 degrees C twice as hot as 5 degrees C?

Please answer in 50 words or less

[TheVisitor]

I have to explain to a friend why the answer to the 2 below questions is 'no'. Any succinct, easy-to-understand suggestions? All I know is that 10 beers is twice as many as 5.

a) Is 10 degrees C twice as hot as 5 degrees C?

b) Is 10 decibels twice as loud as 5 decibels?

Best answer gets a beer from me in Vegas (no, not 10 beers)

[py9jmas]

5 degrees C is -268 degrees kelvin. 10 degrees C is -263 degrees kelvin

The Laws of Thermodynamics predict you can never reach 0 Kelvin (Absolute Zero).

0 Kelvin = -273.15 degrees Celsius
273.15 Kelvin = 0 degrees Celsius

=> 5C ~ 278 Kelvin
and 10C ~ 283 Kelvin
[google.com...]
[google.com...]

[g1smd]

Ummm, I covered that in Item #16.

[bedlam]

Gotta give a resounding 'NO' to both, since they are relative measurements and not quantative

Heat is not quantitative?! Every physicist and mechanical engineer on earth is going to be pretty peeved when they learn that their thermodynamics professors were just making s*** up...

Personally, I always thought they were making thermodyamics up as they went along...

Seriously though, heat is eminently quantifiable. To illustrate the point, it may help to put it into terms of other physical quantities:

1. Energy = work, and work is the product of Force and distance:
   

   w = F(d)

   
   
2. The metric unit of energy is the Joule (J).
   
3. Force is measured in Newtons, and one Newton is equal to 1kg(m)/s²:
   

   1N = 1kg(m)/s[sup]2[/sup]

   
   
4. Distance (obviously) is measured in metres
   
5. So if we substitute force into our equation from (1), we get this:

   • w = F(d), so
     J = Nm
     

     
     
   • so,
     

     
     w = [kg(m)/s[sup]2[/sup]]m
     

     
     
   • Therefore:
     

     
     1J = 1kg(m[sup]2[/sup]/s[sup]2[/sup])
     

So what this tells us, is that if we consider metres, grams and seconds to be measurable, then heat is measurable too.

It also shows that the Kelvin posts in the thread are correct. Temperature, after all, is a measurement of heat energy in a substance, and whether or not absolute zero is reachable, it is still the condition of zero heat and of zero molecular energy. the confusion between 0 degrees Celsius and 0 K comes from not remembering that 0 degrees C is an arbitrary point chosen for convenience, while 0 K is the lower limit of energy.

So we can refer to the total quantity of energy in substances of particular temperatures. Since the C -> K conversion factor is +273.15, 5 degrees C and 10 degrees C are 278.15 K and 283.15 K respectively.

So, in terms of energy, 10 degrees C is not twice as warm as 5 degrees C - and, as the way the question is posed seems to require a quantified answer, it doesn't seem to make much sense to discuss in terms other than energy ;-)

-B

That's about 50 words, right?

[createErrorMsg]

b) Are 10 kids twice as loud as 5 kids? No, they are roughly three times louder. That's how dB works too :)

Oi, if only that were true. I have 28 in my kindergarten class and they're about as loud as 84 kids PLUS three elephants, four howler monkeys, a NYC cab, two turbine engines and a humpback whale. And that's during rest time. Please let me go webdev full time...

[MozMan]

Heat is not quantitative?! Every physicist and mechanical engineer on earth is going to be pretty peeved when they learn that their thermodynamics professors were just making s*** up...

I could be mistaken, but I think there is an inherent difference in the measure of heat (an actual, quantifiable measure of energy) and the measure of temperature, which is not a measure of heat, but instead a measure of a single by-product of heat...

[g1smd]

Anyone want to shed some light on why 0 K is known also as absolute zero then?

[bedlam]

I think there is an inherent difference in the measure of heat (an actual, quantifiable measure of energy) and the measure of temperature, which is not a measure of heat, but instead a measure of a single by-product of heat

This isn't exactly right but you do have a point actually. Heat is the energy of molecular motion in a substance. Temperature is the measure of that heat energy, or more precisely the concentration of heat energy. The difference has to do with specific heat [google.com].

To relate temperature in degrees C to heat in Joules, you can use the following information (simplified a bit; I couldn't find a range of specific heat values for H₂O including absolute zero...):

• A (small 'c') calorie is the amount of energy used to raise the temperature of 1 gram of water by 1 degree C (or 1 K).
  
• There are 4.184 Joules to each calorie:
  

  1 c = 4.184 J

  
  
• 0 K is the state of zero energy.
  
• to raise the temperature of a gram of water (frozen, obviously) by 1 degree C/1 K, we need to add 1 c or 4.184 J of energy. To raise its temperature by 278.15 degrees C, we need to add
  

  278.15(4.184) = 1164 J

  ,
  and to raise its temperature by 283.15 K, we need to add
  

  283.15(4.184) = 1185 J

  
  

But since the (small 'c') calorie is based on water, I've been able to leave out a bit of the calculation above. Not all materials have the same specific heat (i.e. a different amount of energy is required to raise a given substance by the same temperature). Air, for example, has a specific heat about one quarter that of water, and so a given volume of air with the same temperature as a given volume of water is actually less energetic (i.e. less energy is required to raise it to that temperature). So, in other words, a given temperature measures different quantities or concentrations of heat energy, depending on the substance.

Anyway, my original point was meant to be that heat is a) quite definitely quantifiable, and b) can definitely be quantitatively related to temperature. That's still true ;-)

-B

Incidentally, these problems get quite a lot more difficult when humidity is considered as a factor...

[createErrorMsg]

these problems get quite a lot more difficult when humidity is considered

Name one thing, other than sweating, that doesn't.