Comparing Temperatures: Is It Logical?

[pivoxa15]

Does it make sense to say that one object is twice as hot as another object?

For example, a 40 degree object is twice as hot as a 20 degree object.

 

[Homer Simpson]

It would be OK to say that one object's temperature is twice that of another.

To me the word hot brings to mind heat. You can not say that one object has twice as much heat as another. 'Heat' is just a term for the transfer of energy from an object with a higher temperature to an object with a lower one.

In social circles, you can however say that, for instance, Pam Anderson is at least 10 times hotter than Kathy Bates.

 

[Theoretician]

Surely, it is only technically acceptable to say it if the temperatures are measured on an absolute scale (such as the Kelvin scale)?

 

[ZapperZ]

Does it make sense to say that one object is twice as hot as another object?
For example, a 40 degree object is twice as hot as a 20 degree object.

The problem with this question is that you need to put it in the context in which it is being asked. Typically, such a thing is used in casual conversation. In such a case, there's nothing wrong with saying that.

However, in physics, the term "hot" doesn't have any definite meaning. You can talk about "temperature" and "heat" because those quantities are clearly defined. One can say an object has twice the temperature of the other, or an object has twice the heat of the other, since each of these quantities has a clear mathematical description on how it is measured. So when there's well-defined quantity, then talking about something having twice the value will make sense.

Zz.

 

[Danger]

Pam Anderson is at least 10 times hotter than Kathy Bates.

Hey, don't be dissin' my Kath... cripes! What am I saying?!

 

[Homer Simpson]

Best Heat explanation I've seen below. Plus a little something for Danger.

http://www.stardestroyer.net/Empire/Science/Heat-Explanations.html

Consider the following thought experiment: imagine a flask of warm liquid, sitting in an air-conditioned room. Beneath it, you can see an unlit bunsen burner. Inside it, you can see a stirrer which has been switched off. The liquid is warmer than the surrounding air, so it must have been heated, right? Wrong. The liquid is at an elevated temperature, indicating increased internal energy. But there is no way to tell whether this energy came from the bunsen burner or the stirrer. If it came from the bunsen burner, then it entered the liquid as heat. If it came from the stirrer, it entered the liquid as work. Once the energy is inside the liquid, there is no way to tell how it got there.

Therein lies the fundamental definition of heat: heat is not a property of matter, and it is not a type of energy. Heat is a type of energy transfer, just like work. You can perform work on an object, and it can experience an increase in internal or kinetic energy as a result, but it can't "contain" any work. Similarly, you can heat an object, but it can't "contain" any heat.

 

[ZapperZ]

Best Heat explanation I've seen below. Plus a little something for Danger.
http://www.stardestroyer.net/Empire/Science/Heat-Explanations.html

Can you please compare what you accept as the "explanation" for heat with what one can find in a standard Thermodynamics text? Why do you accept something you read off some website more than a Thermo text?

Zz.

 

[pivoxa15]

One can say an object has twice the temperature of the other,
Zz.

If one object was 40 degrees celcius and another 80 degree celcius than the second is twice the temperture of the first.

If we convert these two objects to kelvin, the first one is 313.15K and the second 353.15 so in this repect the second object is not twice the temperture of the first.

We arrive at a contradiction.

 

[Bystander]

If one object was 40 degrees celcius and another 80 degree celcius than the second is twice the temperture of the first.
If we convert these two objects to kelvin, the first one is 313.15K and the second 353.15 so in this repect the second object is not twice the temperture of the first.
We arrive at a contradiction.

No. Celsius and Fahrenheit temperature scales are segments of the Kelvin and Rankine scales, respectively. Neither is useful by itself for correlating physical properties with temperature.

 

[ZapperZ]

If one object was 40 degrees celcius and another 80 degree celcius than the second is twice the temperture of the first.
If we convert these two objects to kelvin, the first one is 313.15K and the second 353.15 so in this repect the second object is not twice the temperture of the first.
We arrive at a contradiction.

That's why I said that one has to talk about this in the proper CONTEXT! I could also use your example and show it is a "contradiction" in many cases, such as saying an object at one location has twice the potential energy as it did in another location, since where I call zero potential energy is arbitrary.

Zz.

 

[vanesch]

If one object was 40 degrees celcius and another 80 degree celcius than the second is twice the temperture of the first.
If we convert these two objects to kelvin, the first one is 313.15K and the second 353.15 so in this repect the second object is not twice the temperture of the first.
We arrive at a contradiction.

Ok, let's try this one: my keyboard is at 50 cm and my screen is at 100 cm. So my screen is twice as far as my keyboard. However, when measured from the wall, my keyboard is at 150cm, and my screen is at 200cm. So now my screen is NOT twice as far as my keyboard. Also a contradiction

 

[Homer Simpson]

I've got the dust off.

Just blew the dust off my thermo text (Fundamentals of Thermodynamics: Sonntag, Borgnakke, Van Wylen) 5th ed.

Def'n of heat, pg 82:

The thermodynamic defn of heat is somewhat different from the everyday understanding of the word. ... Heat is defined as the form of energy that is transferred across the boundary of a system at a given temperature difference between the two systems. That is, heat is transferred from the system at the higher temperature to the system at the lower temperature, and the heat transfer occurs solely because of the temperature difference between the two. Another aspect in the definition of heat is that a body never contains heat. Rather, heat can be identified only as it crosses the boundary.

I think the best thing to get from all this is that saying a bowl of water is 'hotter' than another bowl of water means that the one bowl has more internal kinetic energy of its molecules. Those molecules could have been excited from mechanical work input, heat transfer (conduction, convection,radiation), neutron absorbtion...

As far as the twice as hot thing... just go around saying "oh my, there is a lot of kinetic energy in the air today" or something like that. Kelvin and Rankine scales do go from absolute 0 and up, and these scales can be used to give direct effeciencies of heat engines, for example, so it's likely much more technically correct.

Outside of a thermodynamic and scientific context, it's all semantics. It's like that T-shirt that says: "YOUR RETARDED" When someone corrects you on the grammer, just mutter "you're retarded".

 

[DaveC426913]

What's even dumber is 'twice as cold'.

'It's twice as cold today as it was yesterday!'

 

[Homer Simpson]

Yesterday is what -1 C here and today it is plus 2 C. So it is -2 times as hot.

 

[ZapperZ]

Just blew the dust off my thermo text (Fundamentals of Thermodynamics: Sonntag, Borgnakke, Van Wylen) 5th ed.
Def'n of heat, pg 82:
I think the best thing to get from all this is that saying a bowl of water is 'hotter' than another bowl of water means that the one bowl has more internal kinetic energy of its molecules. Those molecules could have been excited from mechanical work input, heat transfer (conduction, convection,radiation), neutron absorbtion...
As far as the twice as hot thing... just go around saying "oh my, there is a lot of kinetic energy in the air today" or something like that. Kelvin and Rankine scales do go from absolute 0 and up, and these scales can be used to give direct effeciencies of heat engines, for example, so it's likely much more technically correct.
Outside of a thermodynamic and scientific context, it's all semantics. It's like that T-shirt that says: "YOUR RETARDED" When someone corrects you on the grammer, just mutter "you're retarded".

Ah, wonderful. Now look at that definition, and then see if there is such a thing as "energy". If we go by that definition, then every other forms of energy can also be defined that way, i.e. a moving object really doesn't have a "kinetic energy", but rather it has something that can be transferred to another.

We can look at the Thermo's First Law and clearly see that, without work being done on the system, the amount of "heat" being given equals to the amount of change in the internal energy of the system. In turn, this comes right out of the statistical accounting of the speed distribution of the system. If the internal energy is "energy", and the addition of heat increases its energy, then heat is a form of energy on par with KE, PE, Work Done, Internal Energy, etc. To say that heat isn't energy, but just "energy transfer" is like saying that I have money in my bank account, but when I'm transfering money from one account to another, during the transfer, it isn't money.

Zz.

 

[Homer Simpson]

If we go by that definition, then every other forms of energy can also be defined that way, i.e. a moving object really doesn't have a "kinetic energy", but rather it has something that can be transferred to another.

I don't have a great grasp on the concept, but the way I see it is this:

A block is moving. It KE is 1/2 mv^2. How it got that KE is unknown, and does not matter. (could have been collision with other block, could have been gravity)

A bunch of molecules are moving in an object. There KE is also 1/2 mv^2 as a sum. How these molecules got this KE is unknown and does not matter. (could have been in contact with another object whose molecules had greater KE, could have had work applied)

Different energies can be tranferred. 'Heat' is the term for the transfer of molecules Kinetic Energy from one object of a higher temperature to another with lower T.

If the internal energy is "energy", and the addition of heat increases its energy, then heat is a form of energy on par with KE, PE, Work Done, Internal Energy, etc.

Comparing it to electricity terms. The object with a higher internal kinetic energy equates to object with higher voltage. Bring this object in contact with another object with lower voltage. There is a transfer: current. To me the best comparison is that Heat is the Current. The voltages represent internal KE. An object can not pocess current, and nor is current a form of energy. There is not necesarily any work done in the process. I realize this is a fairly weak comparison.

EDIT: OK, scrap the current thing, the more I think of it the more I don't like it.

 

[D H]

The definition Homer quoted from his thermo book is a good one: "a body never contains heat". The concept of a body containing heat, the caloric model of heat is an old idea. The caloric model of heat was gradually discarded over the course of the 19th century because it doesn't work.

The idea of heat content is appealing: just define the total heat content of some object as

$$Q = \int_{\mathrm{absolute\ zero}}^{\mathrm{current\ state}} dQ$$

The concept doesn't work because the amount of heat needed to change the thermodynamic state of an object from state A to state B depends on the path taken between the two states. Because the integral is path dependent, there can be no definitive answer to the question "what is the heat content of object A?"

This means that one cannot say that body A is twice as hot as body B. The bodies can be compared in terms of temperature, enthalpy, free energy, and a host of other thermodynamic state variables, but not heat.

 

[Morbid Steve]

Context, context, context!

 

[skywolf]

couldnt you just say that the average speed of a particle is twice as fast as the speed of another particle, as long as they are the same particle?

 

[pivoxa15]

couldnt you just say that the average speed of a particle is twice as fast as the speed of another particle, as long as they are the same particle?

As we have seen from the examples earlier, it is dangerous to claim twice or any other multiples of the original quantity when comparing the magnitude of a measurement. Look at the celcius and kelvin example.

But if you keep all the units constant throughout or if you like, keep the context constant than you are able to get away with multiples of magnitudes.

 

[Doc Al]

couldnt you just say that the average speed of a particle is twice as fast as the speed of another particle, as long as they are the same particle?

Perhaps you are thinking of this: The Kelvin temperature of a substance is directly proportional to the average kinetic energy of its molecules.

 

[Clausius2]

The definition Homer quoted from his thermo book is a good one: "a body never contains heat". The concept of a body containing heat, the caloric model of heat is an old idea. The caloric model of heat was gradually discarded over the course of the 19th century because it doesn't work.

The idea of heat content is appealing: just define the total heat content of some object as

$$Q = \int_{\mathrm{absolute\ zero}}^{\mathrm{current\ state}} dQ$$

The concept doesn't work because the amount of heat needed to change the thermodynamic state of an object from state A to state B depends on the path taken between the two states. Because the integral is path dependent, there can be no definitive answer to the question "what is the heat content of object A?"

This means that one cannot say that body A is twice as hot as body B. The bodies can be compared in terms of temperature, enthalpy, free energy, and a host of other thermodynamic state variables, but not heat.

I liked very much this post, in part because I have seen in PF many people writting stuffs like $$dQ$$ or $$\Delta Q$$ what is completely false because of the explanation given in this post. Mathematically, and Physically talking, one may write $$\delta Q$$ and $$Q$$ as the substitute of the two former damn expressions, because $$Q$$ is an inexact differential.

Let's see if we can get rid of that kind of things from here forever.

 

[D H]

I liked very much this post, in part because I have seen in PF many people writting stuffs like $$dQ$$ or $$\Delta Q$$ what is completely false because of the explanation given in this post. Mathematically, and Physically talking, one may write $$\delta Q$$ and $$Q$$ as the substitute of the two former damn expressions, because $$Q$$ is an inexact differential.
Let's see if we can get rid of that kind of things from here forever.

Thanks for the plug. But let's not throw out the baby with the bath water, since the baby in this case is the First Law of Thermodynamics. Just remember that entities don't contain heat and that $Q$ always refers to a path-dependent differential.