# Temperature: Does it make sense to say something is twice as cold . (or hot)?

Temperature: Does it make sense to say something is "twice as cold". (or hot)???

Here's an old joke:

If the temperature outside is zero degrees, and if it will be twice as cold tomorrow, what will the temperature be?

The joke doesn't specify if the temperature is given in degrees Fahrenheit or degrees Celsius.

Let us therefore assume, we're talking about 0 degrees Fahrenheit.

Using the fact that : $$\displaystyle{C = \frac{5}{9}(F - 32)}$$

we can enter $$\displaystyle{C = \frac{5}{9}(0 - 32)}$$

and conclude that 0F must equal $$\displaystyle{-17\frac{7}{9}}$$ degrees Celsius

Double that (twice as cold), and you get $$\displaystyle{-35\frac{5}{9}}$$ degrees Celsius.

Convert that back to a Fahrenheit temperature using $$\displaystyle{F = \frac{9C - 32}{5}}$$

and we conclude that "twice as cold" as 0F is apparently -57.6F.

But what then if some day it is -28.8F, what is "twice as cold" then?

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Mute
Homework Helper
You stumbled onto the difference between two kinds of quantitative variables: ratio-level variables and interval level variables. A ratio-level variable is one for which the ratio of two quantities is meaningful (i.e., makes sense). An interval level variable is one for which the ratio doesn't make sense, but the difference between two such variables does.

Temperature, when measured in Celius or Fahrenheit, is an interval level variable, and so it does not make sense to say "the weather report said it will be twice as hot today; it was 25 degrees C yesterday, so that must mean it will be 50 degrees C today!!"

However, when measured in Kelvin, temperature is a ratio-level variable (since it is an absolute scale, I think), so if you measured the temperature to be 273 K (0 deg C) one day and 546 K (273 deg C) the next day, you could say that the temperature was twice as hot as it was yesterday (ignoring the fact that you'd probably be dead from it being 273 deg C out. =P).

With respect to your "twice as cold example", if it were 0 deg C = 273 K, the temp the following day, were it twice as cold (half the previous day's temp) would be 136.5 K = -136.5 deg C.

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polishastro
yeah its a good one alright,
like if one sound is 50dB
how much is twice as loud?

I can not imagine if someone says it's twice as hot or that sound is double.

But it's quite normal when hearing this food is twice as delicious (if its price is 2 times more expensive).

i can imagine something being twice as hot/loud

first of all i'm assuming that when you touch something hot that you nerves send that info to your brain, qualitativly and quantitativly, so i'm guessing that when your temprature transducers produce twice the output and you percieve it as twice as hot?

i know the ears response to sound is logarithmic, i.e. if you make the sound 10 times more energetic, you may not think its gotten much louder at all!!

it would be interesting for someone to plot the percieved response of skin to temprature.

This is one of my pet peeves - I drives me crazy when people say things like "the temperature is 20 percent below normal..." I usually say that "in centigrade its only about 10% low" and I always get blank stares or nervous smiles...

As Mute explains above, it only makes sense for absolute scales.

stewartcs
Mute hit the nail right on the head. One must use absolute scales.

CS

D H
Staff Emeritus
Mute hit the nail right on the head. One must use absolute scales.
I would go further: It doesn't make sense, period, to say that something is twice as hot as something else. Saying this implies that "heat" is a state quantity (e.g., mass charge, temperature, ...) of an object. Heat is a process quantity, not a state quantity. How heat transfer affects the state of objects is path dependent. The concept of heat as state quantity goes back to phlogiston and caloric theories of heat. These are failed theories. Objects do not hold "heat".

stewartcs
I would go further: It doesn't make sense, period, to say that something is twice as hot as something else. Saying this implies that "heat" is a state quantity (e.g., mass charge, temperature, ...) of an object. Heat is a process quantity, not a state quantity. How heat transfer affects the state of objects is path dependent. The concept of heat as state quantity goes back to phlogiston and caloric theories of heat. These are failed theories. Objects do not hold "heat".
Good point. Heat is just an energy transport phenomenon. Objects don't contain heat. Unfortunately, the term is misapplied quite often.

CS

except that the same word can have more than one meaning..

yeah its a good one alright,
like if one sound is 50dB
how much is twice as loud?
+3dB

so 93dB is twice as loud as 90dB and 13dB is twice as loud as 10dB. (in terms of power)

however, the human ear/brain perceives an increase of approximately 6dB to be a doubling of loudness.

if there is continuous noise at one level, the human ear/brain cannot perceive a noise approximately 10dB lower than that noise at the same time.

(someone hit on my field of expertise :D .. [acoustic/vibration engineer])

I would go further: It doesn't make sense, period, to say that something is twice as hot as something else. Saying this implies that "heat" is a state quantity (e.g., mass charge, temperature, ...) of an object. Heat is a process quantity, not a state quantity. How heat transfer affects the state of objects is path dependent. The concept of heat as state quantity goes back to phlogiston and caloric theories of heat. These are failed theories. Objects do not hold "heat".
Are you sure about this DH? My understanding is that how hot something is - is a measure of its internal energy, which is a function of temperature only - a state quantity. So to say something is say twice as hot just means it has twice the internal energy. In terms of temperature scales this ratio (twice) only makes sense using degrees Kelvin. As you say, heat is an energy transfer process, but why do you say that 'how hot' implies that heat is a state quantity?

stewartcs
except that the same word can have more than one meaning..
Not in thermodynamics. The term heat has a very specific meaning.

stewartcs
Are you sure about this DH? My understanding is that how hot something is - is a measure of its internal energy, which is a function of temperature only - a state quantity. So to say something is say twice as hot just means it has twice the internal energy. In terms of temperature scales this ratio (twice) only makes sense using degrees Kelvin. As you say, heat is an energy transfer process, but why do you say that 'how hot' implies that heat is a state quantity?
Temperature is not directly proportional to internal energy since temperature measures only the kinetic energy part of the internal energy, so two objects with the same temperature do not in general have the same internal energy.

The comment by D_H (to me anyway) means that heat is not an intensive or extensive property of a substance (which define the state of a substance). Rather it is a transfer process. He is placing emphasis on the point that objects don't contain heat.

Also the temperature scale only need be absolute, not just Kelvin (i.e. Rankine is fine too).

CS

Temperature is not directly proportional to internal energy since temperature measures only the kinetic energy part of the internal energy, so two objects with the same temperature do not in general have the same internal energy.
Ok stewartcs -thanks. But I'm still a bit confused re this. Having just read up on it again it seems that the internal energy is the sum of the kinetic energy (KE) and potential energy (PE) associated with the random motion of the atoms/molecules of the body. And temperature is a measure of the average *translational* KE. But under the ideal gas aproximation we *define* the IE as a function of temperature only - right? Does this mean we neglect these internal PEs? What about any internal *rotational* KE?

stewartcs
Ok stewartcs -thanks. But I'm still a bit confused re this. Having just read up on it again it seems that the internal energy is the sum of the kinetic energy (KE) and potential energy (PE) associated with the random motion of the atoms/molecules of the body. And temperature is a measure of the average *translational* KE. But under the ideal gas aproximation we *define* the IE as a function of temperature only - right? Does this mean we neglect these internal PEs? What about any internal *rotational* KE?
The Ideal gas assumption accounts for the translational kinetic energy only and not the rotational and vibrational motions. Hence, the temperature is the only factor that affects an ideal gas and it is directly proportional to the average translational kinetic energy.

Hope that helps.

CS

The Ideal gas assumption accounts for the translational kinetic energy only and not the rotational and vibrational motions. Hence, the temperature is the only factor that affects an ideal gas and it is directly proportional to the average translational kinetic energy.Hope that helps.CS
It does. Thanks

Not in thermodynamics. The term heat has a very specific meaning.
I know, but in the previous examples when random people say "twice as hot" they're obviously not talking about thermodynamics!!