Mass And Temperature, Does the mass of an object change w temp

Does the (non-relativeistic) mass of a stationary object change with its temperature.
For example would a stationary bowling ball have a different mass at 100000 degrees C vs if it were at 0 deg C.

Mass is defined to be an invariant quantity, so no, the mass of a body at higher temperature is still the same. I anticipate someone will try to tell you when you heat something up you are increasing it's internal energy and as a result of the energy going up, the mass goes up. The person in my imagination saying that is wrong. Mass does not increase or decrease. It is invariant.

Either way, that is a relativistic effect. In non relativistic mechanics, mass is generally assumed to be invariant. In thermodynamics when you heat something up it's volume can increase, but it's mass will stay the same.

The trouble is that this effect is rather small. The volume of your bowling ball would not change very much even if you heated it up to just below it's melting point. However, the extension by thermal expansion depends on the natural length of a body so you'll see of bridges and rail lines they leave gaps every so often to leave room for the expansion. If you don't the thermal expansion can actually cause the bridge to collapse or the rails of buckle.

Hope this helps.

So you're saying that if a hydrogen atom absorbs a photon, it violates Einsteins law of mass-energy equivalence and retains its former mass? I'm not sure I buy that. The rest masses of isolated particles are invariant, but when together in a system they can interact by means of exchanging virtual particles. In an excited hydrogen atom there will be more virtual particles present and thus will have a higher mass than a ground state hydrogen atom.

But a hydrogen atom in the ground state is not just a single electron and a single proton. It's these two particles plus a cloud of photons that transmit the electromagnetic force. Absorbing a single photon hardly changes the amount of particles at all.

Also remember that the particles that make up matter are never isolated and always have a cloud of photons or other gauge bosons associated with them depending on what forces they couple to. What makes you think there will be more virtual particles in excited hydrogen?

The mass energy equivalence is generally taught like this: mass is a form of energy, therefore mass can be converted into energy. While that is almost true it is very misleading. What would be more correct to say is that a particles invariant mass contributes to it's energy. The particles energy can change (like when it's going very fast) but a particles mass cannot change. When a particle has very high energy we get a deviation from the Newtonian kinetic energy = 1/2 m v^2 The KE of a particles is less than you would expect from Newton at a particular velocity. That can be interpreted (poorly) as an increase in mass. What we know now is that the Newtonian expression for KE is only the first approximation to the relativistic expression for KE.

In actuality, I was thinking of a bulk substance when writing my first reply so this is a bit of a digression. The relativistic mass increase myth is an axe that I like to grind as often as possible though, so thanks for giving me the opportunity.

See the problem there is that that is different from the question being asked.

An increase in temp is an increase in molecular motion. Since mass = density * volume the idea with heating something up is that it will expand increasing in volume but as a result there is also a direct proportional decrease in density. This results in the mass remaining unchanged.

How is it different? The original question was about heating an object. You could heat an object by bathing it in electromagnetic radiation, like toasting bread by having it absorb infrared wavelength photons emitted by hot coils. Heat up a box if hydrogen atoms at low pressure. There - I have basically boiled the original question down to one of the simplest systems possible.

Imagine a photon of energy hc/λ and momentum h/λ being absorbed a hydrogen atom with rest mass m₀ at rest (photon moving in positive direction). The assertion is that the rest mass m₁ of the excited hydrogen atom m₁ is equal to m₀

The relativistic formula for E (with rest mass m):

E = γmc²

E₀ = γ₀m₀m₁ + hc/λ = m₀c² + hc/λ
E₁ = γ₁m₁c²
E₀ = E₁ (conservation of Energy)
γ₁m₁c² = m₀c² + hc/λ
γ₁m₁ = m₀ + h/λc


Relativistic momentum p = γmv (with rest mass m and velocity v):

p₀ = γ₀m₀v₀ +h/λ = h/λ
p₁ = γ₁m₁v₁
p₀ = p₁ (conservation of momentum)
γ₁m₁v₁ = h/λ

Substituting into the energy equation:

γ₁m₁ = m₀ + h/λc
= m₀ + γ₁m₁v₁/c
m₀ = γ₁m₁(1 - v₁/c)

For 0<v₁<c, it can be shown that γ₁(1 - v₁/c)>1, so m₀ < m₁.

Heat up a box of hydrogen and you increase the number of hydrogen atoms in an excited state and hence its mass. Now I could be wrong, but I expect more than a hand waving argument.

Precursor, why would a change in volume mean anything to do with mass? A ton of feathers takes up more volume than a ton of bricks but it's still a ton.

Besides, not all substances always increase in volume with an increase in temperature. Water is densest at 4C. And thankfully too.

This post has been edited by AlphaNumeric on Apr 30 2008, 05:47 AM

Here is the non hand waving argument:

This equation is pure and complete bunk. E = mc² for a particle at rest. E²=(pc)² + (mc²)² for a particles with momentum p. Even if the equation wasn't bunk which it is, the gamma factor for p = 0 is simply 1 so your bunk formula reduces to the correct one anyway.

There's an error in the first step, which doesn't look good to me. I'm going to say this again: In relativity mass is defined as the invariant length of the energy momentum 4 vector. There is no difference between rest mass and dynamical mass.

This post has been edited by prometheus on Apr 30 2008, 08:36 AM

Another reason why the calculation of the mass of an atom + a photon is not a very good model is that atoms and photons are quantum particles. Relativity on it's own doesn't include quantum effects like the cloud of virtual photons I mentioned earlier.

E = γmc² where E is the total energy, and if you don't believe me then you're going to have to start editing some wiki pages. I suggest starting with this one: http://en.wikipedia.org/wiki/Mass-energy_equivalence
You're going to have to change the sentence "If the mass is the relativistic mass, then the energy is the total energy."

We'll see how long your edits stick around. You'll also have to hack into hyperphysics.phy-astr.gsu.edu and change some of their pages too.

Heat is a form of energy, so it does have a mass, of course. Just as chemical or fall height energy, or any other, does.

When writing the energy of a particle, one shouldn't forget terms. Kinetic energy and rest mass are just some of them. Electromagnetic or baryonic interactions would be some other ones, and me may still ignore some of them.

If you want a more detailed insight of heat's mass, at the particle level, it translates to kinetic and electromagnetic energies, which in turn have a mass.

So, divide the number of joules of heat by (3e8)^2 and you get the mass increase in kg. Quite simple scalar computation.

Which won't be much mass.

There was an error in the transcription of my notes. I wrote

E₀ = γ₀m₀m₁ + hc/λ = m₀c² + hc/λ

But it should read

E₀ = γ₀m₀c² + hc/λ = m₀c² + hc/λ

It doesn't change my argument.

And I agree with Enthalpy, it wouldn't be much mass. Still greater than zero.

Citing wikipedia as a source is not going to cut it I'm afraid.

The equation E²=(pc)² + (mc²)² is derived by taking the inner product of a general energy momentum 4 vector with itself. Here is a relevant bit (also on wikipedia): link If you know anything about 4 vectors in special relativity you'll know that when you take the inner product of a vector with itself you get a scalar that is lorentz invariant, that is, it is the same for all inertial frames. It's that clear: mass is a Lorentz invariant and there can be no 2 ways about it.

I have to say I was rather disheartened that hyperphysics was putting out such garbage, which is why I was happy to see this page.

If you're used to thinking like Newton, relativistic mass is a nice way of visualizing what happens at relativistic speeds. If you're actually trying to use relativity to calculate something, it's worse than a useless concept. It's confusing and science can be confusing enough.

Being as I rubbished you (quite rightly) for citing wikipedia, I thought I'd find some better references to support what I'm saying, and lo and behold, what should come up?!

Hyperphysics page on momentum four vectors

If you can't be bothered to read that, here is the relevant section:

In the mouth of two or three witnesses let every word be established, so here is another one from Wolfram scienceworld.

To sum up then, and to directly quote the current head of department where I work, an eminent theoretical physicist, m = γm_0 is a load of <expletive deleted>. I couldn't have put it better myself.

You're really hung up on this relativistic momentum thing, aren't you. I think you're wrong on this point, and one of the reasons is because it is an inelastic collision between two particles and thus you only need to consider 2 dimensions, one of space and one of time. The equations I've been using result from simplifying your 4 momentum. You're trying to make this more complicated than it is. The fact that I solved for the rest mass after the collision apparently escaped you. I'm very aware of the un-value of the concept of relativistic mass.

Anyway, the equation E = γmc² appears in the Invariant Mass section of Chapter 2 in Modern Physics by Tipler and Llewellyn. It's a decent undergraduate text and since you've become quite rusty at this sort of thing, I recommend you brush up before making any more asinine assertions.

I do hope AlphaNumeric or similar physics heavyweight wieghs in on this issue.