States and processes

...and equilibrium, and thermodynamic variables, and more!

"State" of a system

A thermodynamic system is characterized by the values of macroscopic properties, such as pressure $P$, temperature $T$, volume $V$.

  • also called "thermodynamic variables",
  • or "thermodynamic parameters"),
  • These have exact differentials $dV$, $dT$, $dP$... that fulfill the role of coordinates of a system.

Ideal gas: The thermodynamic parameters $P$, $V$, and $T$ are related to each other through this state equation: $$PV=nRT.$$

Thermodynamic variables as coordinates? Consider a constant number of particles $n$ enclosed in a cylinder with a movable piston with adiabatic walls. If you move the system to have some particular values of $V$ and $T$, then $P$ will always be found to be the same (as calculated from the ideal gas law), no matter the path you took to reach $V$ and $T$.

For more complicated systems, we'll eventually add other thermodynamic variables like magnetization $M$. Or we may need to keep track of the amount of two different kinds of chemical species in our system.

Preview of what's to come

Heat $Q$ and work $W$ are not thermodynamic variables. Their differentials are inexact: $\delta Q$, $\delta W$.

But there exists a combination which is exact: $dU = \delta Q - \delta W$ called the internal energy of the system.

Where our convention is $\delta Q > 0$ when heat flows in to the system, from the surroundings. But $\delta W > 0$ means the system does work on the surroundings.

Equilibrium state

An equilibrium state of a system has these characteristics:

  • the system properties (e.g. temperature, pressure, ...) are the same throughout the system (not changing with position).
  • the system properties are constant (not changing with time).

For equilibrium states we can talk about "the" pressure or "the" temperature of the system (it doesn't depend on position or on time).

This course will deal almost exclusively with equilibrium states.

Earth's atmosphere

Is the 'system' consisting of earth's atmosphere in an equilibrium state?

If this is *not* an equilibrium state... shall we conclude that this course (which deals with equilibrium states) will have nothing to say about things like Earth's atmosphere??!!??

No!

Pressure profile of the atmosphere: We know for sure that atmospheric pressure drops as altitude increases.

Let's chop up the atmosphere (a non-equilibrium system) into many small pieces. If the pieces are each small "enough", then it's not a bad approximation to treat each piece as an equilibrium system, with uniform $P$, $V$, $T$, and each piece is in contact with other systems having slightly different thermodynamic parameters.

To do: Start setting up homework problem "Helrich 2.7" (see Homework assignment #1).

Process: change of state

Wait, things can't *change with time* if we're going to talk about equilibrium states!

But we will approximate a time-changing (non-equilibrium!) system as a series in time of equilibrium states: These will be "quasi-static" equilibrium states.

A change of state is often traced out on a $P$-$V$ diagram. This allows you to see where the system is doing work (=$P\,dV$) or having work done *on* it.

4 stroke engineTo do: sketch on a $P$-$V$ diagram the path taken by the system defined as the volume above the piston in the accompanying diagram of the 4-stroke engine.

Number the different parts of the path.

Ignition looks like it happens instantaneously, but this is not a *point* on the $PV$ diagram. Draw what happens *during ignition* as a finite-length path on the diagram as well.

What kind of approximations about the system are being made?

Diagram from "Four-stroke engine" (Wikipedia).

Idealizations: a.) That ignition happens ~instantaneously. b.) Temp/pressure are probably *not* exactly the same throughout the system at all times.

Types of processes

  • Cyclical - Initial and final states are the same.
  • Quasistatic - The state is almost in an equilibrium state: no sudden jumps or drastic changes.
  • Reversible - no friction; no dissipation. (All natural processes are irreversible.)
  • Adiabatic - no heat flows in/out of the system.

Something constant?

Many processes are carried out in such a way that some thermodynamic property is held constant. For example:

  • Isothermal processes take place at a constant temperature.
  • Isobaric processes take place at a constant pressure.
  • Isochoric processes take place in systems in which the volume does not change.

A few other assumptions

There is no significant chemical interaction between the contents of the system and any walls that happen to coincide with the boundaries of the system. We *will* treat the situation where there are chemical reactions happening in the "stuff" of the system.

We'll treat the "stuff" of the system as continuous. Practically, this means we're talking about systems with volumes large compared to typical atomic dimensions:

One mole of an 'ideal' gas at STP contains $6.02 \times 10^{23}$ molecules and has a volume of 22.4 liters $=0.0224 {\rm m}^3$.

One kilomole ($10^3$ moles) contains $6.02 \times 10^{26}$ molecules and has a volume of 22.4 ${\rm m}^3$.

$\Rightarrow$ volume / molecule = $\frac{0.0224 {\rm m}^3}{6.02 \times 10^{23}} = 3.7 \times 10^{-26} {\rm m}^3 = (3.3 \times 10^{-9}{\rm m})^3 = (3.3 \:{\rm nm})^3$.