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_

Unknown macro: {in}

-E_

Unknown macro: {out}

</math>. Taking a time derivative <math>\frac{\partial \Delta E_{sys}}

Unknown macro: {dt}

= \frac{\partial \Delta E_

Unknown macro: {in}

}

-\frac{\partial \Delta E_{out}}

Unknown macro: {dt}

</math>. The flux of energy in is <math>\frac{\partial \Delta E_

Unknown macro: {in}

}

</math>, and the flux of energy out is <math>\frac{\partial \Delta E_{out}}

Unknown macro: {dt}

</math>. Below is a mass conservation relation.

<center>

<br>

<math>\frac

Unknown macro: {Delta m/v}

= -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

Unknown macro: {partial (E/v)}
Unknown macro: {dt}

= -div(J_E)</math>

<br>

</center>

Energy of a system

What is <math>\Delta E_

Unknown macro: {sys}

</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_

Unknown macro: {KE}

+\Delta E_

Unknown macro: {PE}

+\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

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