# Kinetic energy and thermal energy

1. Feb 21, 2006

hello

First question - If only force acting on an object is gravitational force then total mechanical energy TME of system is conserved. What about when two objects, each with it's own kinetic energy, collide in an isolated system?
Is total mechanical energy of a system conserved (the way the momentum is conserved)?

Second question - Moving ball has two types of kinetic energy. One is from the fact that its center of mass is moving (I will call it external kinetic energy) and other type comes from the fact that its molecules are in termal motion. If ball comes to a sudden stop we say that its external kinetic energy is now zero (cchange of kinetic energy is equal to work F*s ). But its internal kinetic energy is still the same.

Do the molecules of a ball receive the energy we call external energy and each molecule gains extra kinetic energy (besides already having its own internal kinetic energy we call thermal energy)?
When the ball comes to a stop then the same amount of external kinetic energy that each molecule gained is now again lost?

And third question - If temperature is a measure of the average kinetic energy, then why are the effects of large kinetic energy of molecules in a body so different from external kinetic energy?

If ball receives a large amount of kinetic energy then this ball gains lots of speed (assuming there is no friction and air resistance). But if internal energy of the ball, as in kinetic energy of molecules ( thermal energy), gains lot of kinetic energy, then besides molecules gaining speed, the ball gets hotter.

My question: Both external and internal kinetic energy (thermal energy) cause an object (external) or molecule (internal) to move faster. But since the type of energy is the same (kinetic), why does internal kinetic energy also cause an object to get hotter while external doesn't ?

thank you

2. Feb 22, 2006

### Hootenanny

Staff Emeritus
For your first question, you are correct if the collision is totally ELASTIC mechanical energy is conserved. However, if the collision is INELASTIC, then some energy is lost as heat and sound etc.

Second question again depends on the type of collision. If the collision is elastic then yes, its internal energy will remain constant. However, if the collision is inelastic, then some energy will transfered to the ball as heat, thus increasing its internal energy.

For your third question, this ventures into the subject of modelling assumptions. Modelling the imperfect world and in a perfect way. That's all I'm willing to say on the subject.

3. Feb 22, 2006

### Staff: Mentor

Right. Mechanical energy is conserved.
Generally, no. KE is only conserved in an elastic collision, which don't occur often in the real world. When KE is lost (macroscopic, ordered KE), the energy is transformed into other types, such as internal energy, sound, and light.

Depending on how the object is stopped, its original macroscopic KE may end up being transformed into increased internal (random) energy or it may end up being transferred to another system.

Better to think of the "external" KE as being macroscopic, ordered KE and the "internal" KE as being random KE (seen from the center of mass frame of the object).

Realize that the internal, random KE of the molecules is measured from the center of mass frame of the object. So it doesn't depend on the object's speed. Any change in the internal energy of the stopped ball depends on how you stop it. For example, toss the ball straight up in the air. It starts out with some internal energy (related to its temperature) and some macroscopic KE. When it gets to the highest point it stops (momentarily), but of course the internal energy hasn't changed.

See my comments above. Temperature is a measure of the random kinetic energy of the molecules in a body as seen from the center of mass frame of the object. It doesn't depend on macroscopic speed.

4. Feb 23, 2006

And that is the reason we only define temperature as a property for a large number of particles that are moving randomly,but can't define it for single molecule?

5. Feb 23, 2006

### Hootenanny

Staff Emeritus
As the number of particle in a body decreases the temperature becomes less meaningful, becasue the average is taken from a reduced dataset.

6. Feb 23, 2006

### Staff: Mentor

Exactly! (As Hootenanny explained.)

7. Feb 23, 2006