# Gasoline traveling fast

1. Jan 29, 2009

### completenoob

I had an odd thought. Suppose I have a ball of gasoline inside a ball of O2 in free space. The ball and I start in the same inertial frame with respect to some planet. The ball starts accelerating. The ball reaches the kinetic energy enough for the combustion of gasoline[I think this will depend on the mass of gas present, but suppose that it is really high and such that the velocity is say 95% the speed of light]. From my frame of reference the ball would explode right?

2. Jan 29, 2009

### JesseM

No, you have to distinguish between linear kinetic energy of the center of mass and thermal energy which is due to the random motion of the molecules in all different directions. Increasing the linear kinetic energy won't cause the molecules in the ball to collide with one another more frequently, for example. All inertial frames make the same predictions about local physical events, so you can't have a situation where one frame predicts it'll explode and another doesn't.

3. Jan 30, 2009

Staff Emeritus
And note that this has absolutely nothing to do with SR. You could write down exactly the same question in Newtonian mechanics and it would have exactly the same answer.

4. Jan 30, 2009

### Naty1

JesseM: Is your explanation the same as here:

http://hyperphysics.phy-astr.gsu.edu/hbase/kinetic/kintem.html#c1

Kudo's if so!!!

5. Jan 30, 2009

### JesseM

The distinction they're making between translational kinetic energy and "internal degrees of freedom such as molecular rotation and vibration" isn't the same as the distinction I was talking about, if that's what you mean--on that page they're still talking about translational kinetic energy of molecules in random directions, which does make the substance hotter (and gasoline closer to exploding) the greater it is, whereas I was talking about the kinetic energy of the system's center of mass, in other words the extent to which the average velocity of all the molecules is pointing in a single direction. On that page I think they're assuming that we're using the rest frame of the center of mass to define the average kinetic energy...

6. Jan 30, 2009

### Naty1

JesseM..yes that's what I meant.....
...so I'm unsure what their answer means...I have never considered whether KE transforms to heat in any way....never heard such a thing....whether high energy particles in colliders, for example, are "hot"...it sounds like from their description "yes" but I'm skeptical...

In other threads length contraction as explained (by DrGreg I think) does NOT result in compression forces and hence no heating....thermodynamics scares me...

7. Jan 30, 2009

### JesseM

Linear kinetic energy of a system's center of mass doesn't transfer to heat, since you can just transform into a different frame where the center of mass of the system is at rest, and different frames can't disagree about local physical questions like whether a ball of gasoline is hot enough to explode. Their point is that at a microscopic level, heat energy is really just due to the random kinetic energy of all the particles making up the system, which have velocities in all different directions--this is a standard idea in statistical mechanics, where temperature for a system at equilibrium can be defined in terms of the average energy per "degree of freedom" (which includes each molecule's freedom to move in any of the three spatial directions, along with rotational and vibrational freedom). I think it's usually assumed in statistical mechanics that we're using the rest frame of the system's center of mass, though.