# The Naked Scientists Forum

### Author Topic: Heavy temperatures?  (Read 3540 times)

#### Tomten

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##### Heavy temperatures?
« on: 16/11/2007 17:50:40 »
Just thinking about Einstein's famous formula linking energy and mass, E=mc2. Since temperature is a form of energy, does it mean that, say, a stone gets heavier as it gets warmer?
Tomten

#### syhprum

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##### Heavy temperatures?
« Reply #1 on: 16/11/2007 21:35:27 »
My venerable sliderule tells me that for every K° you heat the stone its mass will increase by 0.000001534% (it would have to be very hot before you noticed any difference)

#### another_someone

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##### Heavy temperatures?
« Reply #2 on: 16/11/2007 23:13:04 »
My venerable sliderule tells me that for every K° you heat the stone its mass will increase by 0.000001534% (it would have to be very hot before you noticed any difference)

While I agree that the amount of mass increase is very slight, I would ask whether it is actually linear (not having looked at the numbers myself)?

#### lightarrow

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##### Heavy temperatures?
« Reply #3 on: 17/11/2007 00:44:44 »
Just thinking about Einstein's famous formula linking energy and mass, E=mc2. Since temperature is a form of energy, does it mean that, say, a stone gets heavier as it gets warmer?
Tomten

Only if the stone's specific heat doesn't change with temperature. What is proportional to the increase of mass is the energy given to the stone (assuming the stone remain stationary during the process), that is, in this case, the heat you give it.
If, instead, specific heat changes, for example there is a phase transition,  then you give heat to the body (and so its mass increases) while its temperature remains the same.

If you have a stationary body or physical system with a total rest mass M, and you give it some energy E, so that the system remains stationary (for example you can heat it with two beams of electromagnetic radiation or particle beams, coming from opposite directions), then it gains a rest mass m equal to E/c2.
So the new mass is M + m = M + E/c2.

Examples:
1. You give heat to a stat. body.
2. You spin it (with "stationary" I mean that total momentum is zero).
3. You make a cavity with internal reflecting walls, then, through tiny holes, you shoot light beams inside of it.
4. You compress a spring and you let it stay compressed with a clamp. The mass of the system "compressed spring + clamp" is greater than that of the system "non-compressed spring + clamp".

P.S.
Welcome on The Naked Scientists!
« Last Edit: 17/11/2007 00:50:57 by lightarrow »

#### syhprum

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##### Heavy temperatures?
« Reply #4 on: 17/11/2007 09:54:15 »
I did not include specific heat in my calculation therefore I must have assumed it was 1.
I worked via the temperature equivelent of 1 ev, the energy equivelent of 1 ev to give me Joules then applied E=mc^2 to obtain the mass increase.
Is there a more simple way ?.

#### lightarrow

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##### Heavy temperatures?
« Reply #5 on: 17/11/2007 12:25:42 »
I did not include specific heat in my calculation therefore I must have assumed it was 1.
I worked via the temperature equivelent of 1 ev, the energy equivelent of 1 ev to give me Joules then applied E=mc^2 to obtain the mass increase.
Is there a more simple way ?.
If specific heat is the same as water = 1 cal/g*K = 4180 J/kg*K then Δm = 4180/c2 = 4.65*10-14 kg for every K increase of temperature, for every kg of mass of the stone = 4.65*10-12 % = 0.00000000000465 % increase of mass.
« Last Edit: 17/11/2007 12:28:25 by lightarrow »

#### syhprum

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##### Heavy temperatures?
« Reply #6 on: 17/11/2007 14:33:37 »
I suffered an arithmetic block and forgot a direct conversion of calories to Joules.

#### lyner

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##### Heavy temperatures?
« Reply #7 on: 19/11/2007 10:21:43 »
I think this mixing of classical and relativistic ideas is on a hiding to nowhere. The statistics of a system which is hot enough to be getting in the region of E = mcsquared  for particles, is going to affect the 'specific heat capacity'. You would be in the range of plasma behaviour and any energy put in would certainly not  just go into translational KE.
Newtonian sums go out of the window and so would the simple kinetic theory calculations. The population of particle energies would be nothing like the classical model.
Here be dragons.
« Last Edit: 19/11/2007 10:25:48 by sophiecentaur »

#### lightarrow

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##### Heavy temperatures?
« Reply #8 on: 19/11/2007 14:00:47 »
I think this mixing of classical and relativistic ideas is on a hiding to nowhere. The statistics of a system which is hot enough to be getting in the region of E = mcsquared  for particles, is going to affect the 'specific heat capacity'. You would be in the range of plasma behaviour and any energy put in would certainly not  just go into translational KE.
Newtonian sums go out of the window and so would the simple kinetic theory calculations. The population of particle energies would be nothing like the classical model.
Here be dragons.
It's true that at "normal" temperatures the increase of mass is (almost certainly) negligible with the present measurement technology; those computations are theoretical (at the moment).

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##### Heavy temperatures?
« Reply #8 on: 19/11/2007 14:00:47 »