Pressure and Temperature

We are now turning our attention to the microscopic world of molecular motion to see that the same concepts that we have been talking about, still apply.

To begin with, we defined

Pressure = Force/Area

which now explains why the steel balls broke the seal more easily than the tennis balls. They simply applied more pressure to the surface because they had a smaller area of content.

Recall now that we have defined a force, in terms of Newton's Second Law, as the rate of change of the momentum of an object.

So Force = change in momentum/change in time

If pressure is force/area, then pressure really represents a momentum change distributed over some area. Now we can understand our balloon.

Imagine that we can keep the volume of the balloon constant. What happens if we increase the temperature of the balloon?

Well the pressure rises, of course, but why is this the case?

An increase in pressure means an increase in the force per unit area or an increase in the rate of change of momentum of the balloon, but what causes this?

After a while we figured out that temperature was a measure of the random velocity of a molecule. Higher temperatures mean higher velocities.

Well, if there are higher velocities then that means the rate at which molecules collide with the balloon wall is higher. There are more collisions per unit time.

To understand that this effects the pressure means that the collisions between the molecules and the wall of the balloon must be the source of pressure. Since pressure is force per unit area, and the area is constant, then the force is greater meaning the rate of momentum change is greater. In effect, the molecules transfer momentum to the balloon wall each time there is a collision.

Now we can understand Heat flow in a System (java applet link).

We ran this in class and determined the following:

• heat flows from higher temperature to lower temperature.
• Thermodynamic equilibrium always occurs
• When the system is in equilibrium their are equal numbers of particles on both sides of the box.

The physics that drives the heat flow can be related to pressure. The particles on the hotter side have a higher pressure and this causes a net flow of particles from the hot to the cold side.

We can imagine putting some kind of device where the membrane is that separates the chambers that feels the pressure flow of the molecules on it and converts that into energy.

In essence, this is the principle behind the thermodynamic heat engines that were demonstrated in class. The hot side of the heat engine generated a net flow of molecules and those molecules collided with a semiconductor material. Those collisions liberated electrons in the semiconductor and a current was created which powered the motor.

The Key point is that as long as their is a temperature difference between the two sides, there will be a pressure difference from which work can be derived.

The efficiency of the heat engine is given by:

1 - t₁/t₂ where t₂ > t₁; all temperatures here are on the Kelvin Temperature Scale

The principle of a heat engine, in fact, can be applied to the world's oceans to help solve our energy problem. This is known as OTEC and you should go read this lecture