Tuesday, February 19, 2013

Introduction to Thermodynamics

Thermodynamics comes from the study of steam engines, so we'll often be seeing engines as examples.

Fundamentally, we study a system. A system is the collection of "stuff" that we want to know about. The system has some boundaries - they could be real or theoretical. Everything outside this boundary is the universe.

There are some important properties of the boundaries that we need to know to classify the system. A diathermal system has boundaries which let heat thought. An adiabatic system does not. In an open system, the boundaries between the system and the universe let matter move through them. A closed system is the opposite - the system is isolated from the universe.

We also need to know about the system's state. In our case, with simple systems, we can classify state with a few parameters - namely, pressure, volume, and temperature - the so-called PVT of the system. It's also useful to know the mass of the stuff in our system.

Volume is an easy parameter to understand. Pressure may be a bit trickier. When we talk about pressure, we talk about hydrostatic pressure. In principle this is like the pressure from an unmoving liquid - uniform. Pressure's SI units are Pascals (Pa), which is $Nm^{-2}$ - force over some area - but is often quoted in bars or atmospheres ($10^5$ Pa) or Torr (pressure exerted from a millimeter of mercury. 760 Torr is one atmosphere).

Temperature is also a bit harder to pin down. What does temperature mean exactly? How do we measure it? Perception of temperature is based on the thermal conductivity of the material you're touching - so how do we find the temperature of an item without that getting in the way? What's important to cover first is the concept of thermal equilibrium. Two objects are in thermal equilibrium if they both have the same temperature (which we haven't fully defined yet but bear with me). Basically when we take two objects of different temperature and put them into contact, this property of temperature changes, a change that slows and eventually stops. When this happens the two objects are in thermal equilibrium. In fact, in much of the analysis we'll do we'll require the system to be in thermal equilibrium.

The dynamics of thermodynamics comes up when we put our system through some process. This is how we change our system, and what we'll be studying. The favored type of process is a quasistatic process - one which has such a slow effective change that it's almost doing nothing. This is, of course, an idealization.

Let's look at an example. Say we have some object with temperature $T_1$, which we drop into a reservoir of temperature $T_2$ (a reservoir is a body of stuff that is so large that objects placed in it will not change the reservoir's temperature). The object comes into thermal equilibrium with the reservoir over time. If this change is quick (let's say we drop a burning hot piece of metal into a lake), this is a non-quasistatic process. However, if the rate of change is slower - a gentle transition between $T_1$ and $T_2$, then the process is quasistatic.

When we study a system as we change parameters, we really don't want to change more than one at a time - this makes it hard to tell which change is having which effect. So we hold certain parameters constant. There are fancy names for this:

Finally, it's also important to classify whether or not a process is reversible. That is, if we reverse the order of the steps of the process, does the state of the system go back to the state before this step? A reversible process must be quasistatic. Any non-quasistatic process cannot be reversed. This is an important property.