The book will be on reserve in the library. The class members do not need to study in depth all of chapter 1 ��� 4.
Equation of state
The equations of state that define a relationship between variables are not part of the framework of thermodynamics. The equation of state of an ideal gas is below. Other equations may contain electrical or magnetic constants.
<center>
<br>
<math>pV = nRT</math>
<br>
</center>
Equation of state
The first law involves the conservation of energy, and this can be a difficult concept. Track energy flows in and out.
<p>
</p>
The balance of fluxes in and out is labeled ��E and is expressed as <math>E_
-E_
</math>. Taking a time derivative <math>\frac{\partial \Delta E_{sys}}
= \frac{\partial \Delta E_
}
-\frac{\partial \Delta E_{out}}
</math>. The flux of energy in is <math>\frac{\partial \Delta E_
}
</math>, and the flux of energy out is <math>\frac{\partial \Delta E_{out}}
</math>. Below is a mass conservation relation.
<center>
<br>
<math>\frac
= -div(J_m)</math>
<br>
</center>
What does the divergence mean? It is the difference of flux at <math>x</math> and <math>x + dx</math>. The expression of mass conservation is the same idea as in the 1st law.
<center>
<br>
<math>\frac
= -div(J_E)</math>
<br>
</center>
Energy of a system
What is <math>\Delta E_
</math>? How can a system change its energy? It can change kinetic energy, gravitational energy, potential, or internal energy. The energy of a system is defined below.
<math>\Delta E_
=\Delta E_
+\Delta E_
+\Delta U</math>
<p>
</p>
For stationary systems, the <math>\Delta E_
</math> is zero, and the potential and kinetic energy can be lumped together with the internal energy. The internal energy involves all energy that is internal to the system. For instance, the gas in the car and the charge in the battery contribute to the internal energy. Some energy gets stored in microscopic degrees of freedom. A physicist is concerned with how internal energy is stored. Kinetic energy and potential energy is stored in bonds at the microscopic level.
<p>
</p>
Variables describe the state of a system. A key concept is that the internal energy is defined by the state of the system. There can���t be multiple values of energy associated with a given state.
Energy flows
Work, heat, and matter are associated with energy flows. The flow of energy by work and heat flow is not necessarily associated with matter. The flow of matter is a trivial energy flow. An example is joining systems, such as putting fuel in a car.
Work
Work is the transfer of energy by a ���displacement��� under a ���force.��� Below are different types of work.
- Mechanical: Force times displacement
- Electrical: Electric field times charge
- Magnetic: Applied field times change in magnetization
The infinitesimal displacement vector is <math>dr</math>. Electric work involves displacing charge, <math>dq</math>, over a potential. Magnetic work results from the change in magnetization under an applied field. Quantities are per volume in electromagnetism. Work can also result from the flow of matter (<math>\mu_i</math>, <math>dN_i</math>). The chemical potential is <math>\mu_i</math>, and <math>dN_i</math> is the change in mole number.
<p>
</p>
In general, work results from the displacement of an extensive quantity. The force is labeled ���<math>Y</math>���, and the response is ���<math>dX</math>���. The units of the product of the pair of variables are