Leaving cert physics notes... must know information

robbiep94

One of the fundamental thermodynamic equations is the description of thermodynamic work in analogy to mechanical work, or weight lifted through an elevation against gravity, as defined in 1824 by French physicist Sadi Carnot. Carnot used the phrase motive power for work. In the footnotes to his famous On the Motive Power of Fire, he states: “We use here the expression motive power to express the useful effect that a motor is capable of producing. This effect can always be likened to the elevation of a weight to a certain height. It has, as we know, as a measure, the product of the weight multiplied by the height to which it is raised.” With the inclusion of a unit of time in Carnot's definition, one arrives at the modern definition for power:

During the latter half of the 19th century, physicists such as Rudolf Clausius, Peter Guthrie Tait, and Willard Gibbs worked to develop the concept of a thermodynamic system and the correlative energetic laws which govern its associated processes. The equilibrium state of a thermodynamic system is described by specifying its "state". The state of a thermodynamic system is specified by a number of extensive quantities, the most familiar of which are volume, internal energy, and the amount of each constituent particle (particle numbers). Extensive parameters are properties of the entire system, as contrasted with intensive parameters which can be defined at a single point, such as temperature and pressure. The extensive parameters (except entropy) are generally conserved in some way as long as the system is "insulated" to changes to that parameter from the outside. The truth of this statement for volume is trivial, for particles one might say that the total particle number of each atomic element is conserved. In the case of energy, the statement of the conservation of energy is known as the first law of thermodynamics.
A thermodynamic system is in equilibrium when it is no longer changing in time. This may happen in a very short time, or it may happen with glacial slowness. A thermodynamic system may be composed of many subsystems which may or may not be "insulated" from each other with respect to the various extensive quantities. If we have a thermodynamic system in equilibrium in which we relax some of its constraints, it will move to a new equilibrium state. The thermodynamic parameters may now be thought of as variables and the state may be thought of as a particular point in a space of thermodynamic parameters. The change in the state of the system can be seen as a path in this state space. This change is called a thermodynamic process. Thermodynamic equations are now used to express the relationships between the state parameters at these different equilibrium state.
The concept which governs the path that a thermodynamic system traces in state space as it goes from one equilibrium state to another is that of entropy. The entropy is first viewed as an extensive function of all of the extensive thermodynamic parameters. If we have a thermodynamic system in equilibrium, and we release some of the extensive constraints on the system, there are many equilibrium states that it could move to consistent with the conservation of energy, volume, etc. The second law of thermodynamics specifies that the equilibrium state that it moves to is in fact the one with the greatest entropy. Once we know the entropy as a function of the extensive variables of the system, we will be able to predict the final equilibrium state. (Callen 1985)


The first and second law of thermodynamics are the most fundamental equations of thermodynamics. They may be combined into what is known as fundamental thermodynamic relation which describes all of the thermodynamic properties of a system. As a simple example, consider a system composed of a number of p different types of particles and has the volume as its only external variable. The fundamental thermodynamic relation may then be expressed in terms of the internal energy as:

Some important aspects of this equation should be noted: (Alberty 2001), (Balian 2003), (Callen 1985)
The thermodynamic space has p+2 dimensions
The differential quantities (U, S, V, Ni) are all extensive quantities. The coefficients of the differential quantities are intensive quantities (temperature, pressure, chemical potential). Each pair in the equation are known as a conjugate pair with respect to the internal energy. The intensive variables may be viewed as a generalized "force". An imbalance in the intensive variable will cause a "flow" of the extensive variable in a direction to counter the imbalance.
The equation may be seen as a particular case of the chain rule. In other words:

from which the following identifications can be made:



These equations are known as "equations of state" with respect to the internal energy. (Note - the relation between pressure, volume, temperature, and particle number which is commonly called "the equation of state" is just one of many possible equations of state.) If we know all p+2 of the above equations of state, we may reconstitute the fundamental equation and recover all thermodynamic properties of the system.
The fundamental equation can be solved for any other differential and similar expressions can be found. For example, we may solve for dS and find that


here are many relationships that follow mathematically from the above basic equations. See Exact differential for a list of mathematical relationships. Many equations are expressed as second derivatives of the thermodynamic potentials (see Bridgman equations).
[edit]Maxwell relations
Maxwell relations are equalities involving the second derivatives of thermodynamic potentials with respect to their natural variables. They follow directly from the fact that the order of differentiation does not matter when taking the second derivative. The four most common Maxwell relations are:


The thermodynamic square can be used as a tool to recall and derive these relations.
[edit]Material properties
Main article: material properties (thermodynamics)
Second derivatives of thermodynamic potentials generally describe the response of the system to small changes. The number of second derivatives which are independent of each other is relatively small, which means that most material properties can be described in terms of just a few "standard" properties. For the case of a single component system, there are three properties generally considered "standard" from which all others may be derived:
Compressibility at constant temperature or constant entropy

Heat capacity at constant pressure or constant volume

Coefficient of thermal expansion

tragic and blonde

If this is something we have to know for the leaving a lot of us are in deep ... Something ...

Ah Here!

Yeah none of that is actually on the syllabus. That's far more advanced physics than anything on the leaving cert.

**Timbuk2**

OP, that is all a bit theoretical and advanced for Leaving Cert Physics - definitely not 'must know' for the exam.

For those who are interested, this is the Leaving Cert Physics syllabus - it is quite a good one, and would also serve as a good revision list!
http://www.education.ie/servlet/blobservlet/lc_physics_sy.pdf?language=EN

I also found the notes on this site good for summarising the chapters in the book for LC Physics - you can even download the definitions spoken aloud as an mp3 and put them on your ipod, listen to them while on the bus or something!
http://www.thephysicsteacher.ie/

I'm going to lock this thread, as the first post seems to be just a copy and paste of http://en.wikipedia.org/wiki/Thermodynamic_equations and not all that relevant to LC Physics.