Thermodynamics: Understanding Temperature

[mynoduesp]

just started thermodynamics(12th grade) and need this concept clear

 

[ZapperZ]

just started thermodynamics(12th grade) and need this concept clear

Please use the definition given in your text or in your search. It would be easier to start with something you have in front of you than start cold.

http://hyperphysics.phy-astr.gsu.edu/hbase/thermo/temper.html

I strongly suggest you bookmark the hyperphysics website for future question like this.

Zz.

 

[Hobold]

Temperature is, actually, a very complex definition and I think you would need more than 12th grade physics to understand. Basically you can think of temperature as the degree of agitation of molecules that compose a certain substance. The higher the degree of agitation is, higher is temperature, because molecules will collide more energetically and will also have higher kinetic energy.

Though this definition is very informal, it will take time to understand a better concept. If you have had some thermodynamics in the past, you can also think of temperature as the coefficient that correlates two different systems in thermal equilibrium by an isothermal curve.

 

[Fredrik]

These are two of my old posts about this:

Temperature is the quantity that tells you which way energy will flow when two systems are put into contact with each other. (Energy flows from the system with the higher temperature to the system with the lower temperature).

Let Ω be the number of accessible states. (This is the number of states that the system can change into from its current state). The entropy of the system is defined as the logarithm of the number of accessible states, times a constant: S=k_B log Ω. The reason for the logarithm in the definition is that if system 1 has Ω₁ accessible states and system 2 has Ω₂ accessible states, the combined system has Ω₁Ω₂ accessible states, so the entropy of the combined system is

$$S_{\text{tot}}=k_B\log(\Omega_1\Omega_2) =k_B\log\Omega_1+k_B\log\Omega_2=S_1+S_2$$

The logarithm is what makes entropy an additive quantity. The constant (which is called Boltzmann's constant) is irrelevant to what I'm saying in this post.

[...]

Note that a system must have time to settle to an equilibrium state before the temperature is well-defined. When two systems with different temperatures are put into contact, the temperature of the combined system isn't well-defined until energy has stopped flowing from one the systems to the other.

I forgot about how easy it is to motivate this definition...

Consider two systems that are put in thermal contact with each other. If we keep them isolated from other systems, the total energy is $E=E_1+E_2$ and the total entropy is $S(E)=S(E_1)+S(E_2)$. Energy will flow from one system to the other if that increases the total entropy of the combined system. Let's say that the total entropy increases when energy flows from system 1 to system 2. That means that

$$0<\frac{d}{dE_2}(S_1(E-E_2)+S_2(E_2))=-S_1'(E_1)+S_2'(E_2)$$​

$$\frac{1}{S_1'(E_1)}>\frac{1}{S_2'(E_2)}$$​

This shows that the energy flows from the system with the higher value of $1/S_i'(E_i)$ to the one with the lower value. We therefore define the temperature at energy E of a system with entropy S(E) as

$$T(E)=\frac{1}{S'(E)}$$​

 

[Haldhad]

Temperature is, actually, a very complex definition and I think you would need more than 12th grade physics to understand. Basically you can think of temperature as the degree of agitation of molecules that compose a certain substance. The higher the degree of agitation is, higher is temperature, because molecules will collide more energetically and will also have higher kinetic energy.

Though this definition is very informal, it will take time to understand a better concept. If you have had some thermodynamics in the past, you can also think of temperature as the coefficient that correlates two different systems in thermal equilibrium by an isothermal curve.

Quite I was reading into this recently and as a layman although I have some Freshman calculus, the actual definition was filled with a lot of unknowns and a fair few philosophical ideas. That said at 12th grade I think the simplified idea of what temperature is suffices. It's not quite right, but it suffices.

Boltzman was one very scary and mixed up dude, clever but perhaps too precise with some concepts: entropy is a frightening concept to work with. I mean what is more or less organised, what is states that are more or less mixed unless they are arbitrary. And how does maths deal with integrations that really are more philosophy than maths anyway. I'm not saying the term isn't precise, I'm just saying explained purely from very base values on an atomic scale it all seems rather complicated. Be precise in exactly what you mean to be talking about. A phonon, is what, and temperature is what in relation to this individual entity in a statistic ensemble? Not something I should of dabbled in I think at my level. The calculus is ok, but the overarching questions have driven more than one scientist to despair and even insanity.

Fear not though, the maths works and works well when in a self contained environment, the philosophy is not relevant. Thankfully.

As others said, the key idea is to realize that temperature works in a gradient, so that heat is applied from one medium to another, when thermally self contained the maths works explicitly and well.

 

[hillzagold]

In 12th grade, probably. Dealing with substances, a normal person would consider the average temperature (This block of wood is room temperature). With liquids, you'll think of parts of the liquid (top or bottom, close or far from a heat source) to have varied temperature, but I doubt you'll get down to individual molecules.
To remind you all that first impressions usually stick to a person, I still rely on my 6th grade definition: Temperature is measured by how fast a piece of matter is vibrating and what kind of matter it is.

 

[cjl]

One relatively straightforward definition is that temperature is a measure of the average kinetic energy per particle of a substance.

 

[Haldhad]

One relatively straightforward definition is that temperature is a measure of the average kinetic energy per particle of a substance.

I've been told that using the term average is wrong by some people. I know not why, since obviously this is a correct definition. Temperature is not something that reflects an individual event in a medium, it is something that is attributed to the medium over all.

I quite agree that is a good way of putting it. But some people don't like the term average. I think there is a disconnect between university and something else with some people. I am still not sure why the term average is contentious, I am told as it regards temperature it is by some. I still don't understand why, given the calculus above as proposed. It's probably a semantics issue.

Sorry I know this is above the level of 12th grade but some peoples opinions genuinely have me puzzled.

 

[timthereaper]

I would agree with cjl on this. Temperature can be described as the average kinetic energy per particle of a substance and since you are starting thermodynamics, this is a good definition to start with. As you progress more into thermodynamics, your definition will expand and you'll understand more about why your question isn't the easiest to completely explain.

 

[prajor]

One relatively straightforward definition is that temperature is a measure of the average kinetic energy per particle of a substance.

Basically you can think of temperature as the degree of agitation of molecules that compose a certain substance. The higher the degree of agitation is, higher is temperature, because molecules will collide more energetically and will also have higher kinetic energy.

Both these "definitions" are counter intuitive. Obviously the KE of liquids is more than that of solids, at the SAME temperature. How can this be explained ?

 

[Haldhad]

Both these "definitions" are counter intuitive. Obviously the KE of liquids is more than that of solids, at the SAME temperature. How can this be explained ?

Degrees of freedom, solids are bound in a "lattice", liquids are not, hence it takes more energy to move a solid "lattice" of bonded atoms than freely motive particles, hence the energy may be the same and the overall/average energy consistent with a liquid but the kinetic/movement energy may differ discretely. Hence average temperature makes sense, it is not defined by one type of energy.

That'd be my guess. And it is a guess.

 

[ZapperZ]

Both these "definitions" are counter intuitive. Obviously the KE of liquids is more than that of solids, at the SAME temperature. How can this be explained ?

Er.. how do you know this? It is not "obvious" to me.

The SPREAD in the energy might be larger for a liquid, i.e. the Maxwell-Boltzmann distribution for it might be wider than a corresponding solid at the same temperature, but the AVERAGE (which is what was stated) value can still be the same!

Zz.

 

[Andrew Mason]

I would agree with cjl on this. Temperature can be described as the average kinetic energy per particle of a substance and since you are starting thermodynamics, this is a good definition to start with. As you progress more into thermodynamics, your definition will expand and you'll understand more about why your question isn't the easiest to completely explain.

Temperature is a measure of the average translational kinetic energy of the molecules of a substance. The translational kinetic energy refers to the motion of the centres of mass of the molecules of a substance. It is the motion of the centres of mass of the molecules that allows molecular kinetic energy to be transferred from one molecule to another, which, macroscopically is heat flow.

Rotational or vibrational motion of molecules of an ideal gas does not factor into the temperature of the gas. Vibrational motion of molecules does factor into the temperature of a liquid or solid. This is because the molecules are physically close together so these vibrations cause movement of the centres of mass of molecules - and thus energy to be transferred from one molecule to another.

AM

 

[timthereaper]

Thanks for that correction, Andrew. That is a pretty important distinction I left out.

 

[russlhenley]

Temperature is an English word which very poorly describes the complexities of the physical world. Therefore it is a "non-definitive conceptual representation which is defined relative to the desired outcome of the theory"...to quote my old physics professor.

 

[atyy]

Temperature is a property of a system such that if two systems have the same temperature, the properties of each system will not change when they are put in contact. This is the same as Fredrik's definition in post #4.

For example, let A be a mercury thermometer and B be your body.

When you put a thermometer into your mouth, the length of the mercury thread will increase. When the length of the mercury thread stops increasing, then we say that the the thermometer and your body are at the same temperature.

There is some ambiguity to this, since the "properties" of a system here don't refer to fundmental, microscopic quantities like the position and velocity of each particle in the system, but to coarse, macroscopic quantities like length, volume, pressure.

Also, "will not change" doesn't really mean will never change, since if you leave a thermometer long enough in a person's mouth, the length of the thread will keep on changing depending on whether the person is sitting or running or doing something else. So "will not change" just means will not change over a duration that is long compared to the period of observation.

A good simple reference is Benjamin Crowell's http://www.lightandmatter.com/html_books/0sn/ch05/ch05.html#Section5.1
More advanced references are:
Thomas Greytak http://ocw.mit.edu/courses/physics/8-044-statistical-physics-i-spring-2008/lecture-notes/ (lecture 9)
Mehran Kardar http://ocw.mit.edu/courses/physics/8-333-statistical-mechanics-i-statistical-mechanics-of-particles-fall-2007/lecture-notes/ (lecture 1)

 

[prajor]

Er.. how do you know this? It is not "obvious" to me.

Zz.

Only reasoning that I used was since "Temperature is a measure of the average translational kinetic energy of the molecules of a substance. " , we have more translation in liquid than solid. Hence it is counter-intuitive. I know there is something more to it than that... :)