|Thermodynamics and Propulsion|
Changes in the state of a system are produced by interactions with the environment through heat and work, which are two different modes of energy transfer. During these interactions, equilibrium (a static or quasi-static process) is necessary for the equations that relate system properties to one-another to be valid.
transferred due to temperature differences only.
With the material we have discussed so far, we are now in a position to describe the Zeroth Law. Like the other laws of thermodynamics we will see, the Zeroth Law is based on observation. We start with two such observations:
These closely connected ideas of temperature and thermal equilibrium are expressed formally in the ``Zeroth Law of Thermodynamics:''
Zeroth Law: There exists for every thermodynamic system in equilibrium a property called temperature. Equality of temperature is a necessary and sufficient condition for thermal equilibrium.
The Zeroth Law thus defines a property (temperature) and describes its behavior1.3.
Note that this law is true regardless of how we measure the property temperature. (Other relationships we work with will typically require an absolute scale, so in these notes we use either the Kelvin or Rankine scales. Temperature scales will be discussed further in Section 6.2.) The zeroth law is depicted schematically in Figure 1.8.
[VW, S & B: 4.1-4.6]
Section 1.3.1 stated that heat is a way of changing the energy of a system by virtue of a temperature difference only. Any other means for changing the energy of a system is called work. We can have push-pull work (e.g. in a piston-cylinder, lifting a weight), electric and magnetic work (e.g. an electric motor), chemical work, surface tension work, elastic work, etc. In defining work, we focus on the effects that the system (e.g. an engine) has on its surroundings. Thus we define work as being positive when the system does work on the surroundings (energy leaves the system). If work is done on the system (energy added to the system), the work is negative.
Consider a simple compressible substance, for example, a gas (the system), exerting a force on the surroundings via a piston, which moves through some distance, (Figure 1.9). The work done on the surroundings, , is
Why is the pressure instead of ? Consider (vacuum). No work is done on the surroundings even though changes and the system volume changes.
Use of instead of is often inconvenient because it is usually the state of the system that we are interested in. The external pressure can only be related to the system pressure if . For this to occur, there cannot be any friction, and the process must also be slow enough so that pressure differences due to accelerations are not significant. In other words, we require a ``quasi-static'' process, . Consider .
and the work done by the system is the same as the work done on the surroundings.
Remember this result, that we can only relate work done on surroundings to system pressure for quasi-static (or reversible) processes. In the case of a ``free expansion,'' where (vacuum), is not related to (and thus, not related to the work) because the system is not in equilibrium.
We can write the above expression for work done by the system in terms of the specific volume, ,
where is the mass of the system. Note that if the system volume expands against a force, work is done by the system. If the system volume contracts under a force, work is done on the system.
For simple compressible substances in reversible processes, the work done can be represented as the area under a curve in a pressure-volume diagram, as in Figure 1.11(a).
Key points to note are the following:
How do we know when work is done? (MP 1.3)
Consider Figure 1.12, which shows a system undergoing quasi-static processes for which we can calculate work interactions as .
Along Path a:
Along Path b:
Given a piston filled with air, ice, a bunsen burner, and a stack of small weights, describe
Consider the quasi-static, isothermal expansion of a thermally ideal gas from , to , , as shown in Figure 1.13. To find the work we must know the path. Is it specified? Yes, the path is specified as isothermal.
The equation of state for a thermally ideal gas is
where is the number of moles, is the Universal gas constant, and is the total system volume. We write the work as above, substituting the ideal gas equation of state,
also for , , so the work done by the system is
or in terms of the specific volume and the system mass,
We can have one, the other, or both: it depends on what crosses the system boundary (and thus, on how we define our system). For example consider a resistor that is heating a volume of water (Figure 1.14):