Text 5. The limits of applicability of classical theory

(from Quantum Physics Berkeley physics course-v.4 by Eyvind H. Wichmann, Mcgraw-hill book Co. MW, 1971)

1) Inthe theory of special relativity the velocity of light plays a fundamental role. This velocity, с = 3 x 10¹⁰ сm/sec, is the upper limit on the velocity of any material particle and the upper limit on the velocity by which energy or information can be transmitted in physical space. The existence of this velocity provides us with a simple and natural criterion in terms of which we can decide when a physical phenomenon may be discussed "non-relativistically" and when it must be discussed "relativistically." Roughly speaking a non-relativistic treatment is adequate, i.e., sufficiently accurate, whenever all relevant velocities are small compared to the velocity of light.

2) We may ask whether an analogous criterion exists which tells us when we must apply quantum mechanics and when the theory of classical physics is adequate. Is there a constant of nature, "analogous" to the constant c, in terms of which the desired criterion may be formulated?

3) Such a constant does exist, and it is known as Planck's constant. It is denoted by h, and it has the value

 

4) The physical dimension of this constant is thus [time] X [energy] = [length] x [ momentum ] = [angular momentum]. Such a physical quantity is known as action, and accordingly Planck's constant is also called the (fundamental) quantum of action.

5) The criterion is roughly the following. If for a physical system any "natural" dynamical variable f which has the dimension of action assumes a numerical value comparable to Planck's constant h, then the behavior of the system must be described within the framework of quantum mechanics. If, on the other hand, every variable having the dimension of action is very large when measured against h, then the laws of classical physics are valid to sufficient accuracy.

6) We emphasize that this is a rough criterion which merely tells us when we have to be careful. The fact that an action variable is small in any particular case does not necessarily mean that classical theory is totally inapplicable. In many cases classical theory will give us at least some insight into the behavior of the system, especially if tempered by some quantum-mechanical notions.

 

Text 6. Condensation

(from Conceptual Physics by Paul G. Hewitt, City College of San Francisco, Pearson International Edition, 2006)

1) The opposite of evaporation is condensation—the changing of a gas to a liquid. When gas molecules near the surface of a liquid are attracted to the liquid, they strike the surface with increased kinetic energy and become part of the liquid. In collisions with low-energy molecules in the liquid, excess kinetic energy is shared with the liquid, increasing the liquid temperature. Condensation is a warming process.

2) A dramatic example of the warming that results from condensation is the energy released by steam when it condenses —a painful experience if it condenses on you. That's why a steam burn is much more damaging than a burn from boiling water of the same temperature; the steam releases considerable energy when it condenses to a liquid and wets the skin. This energy release by condensation is utilized in steam heating systems.

3) Steam is water vapor at a high temperature, usually 100 degrees Centigrade or more. Cooler water vapor also releases energy when it condenses. In taking a shower, for example, you're warmed by condensation of vapor in the shower region—even vapor from a cold shower—if you remain in the moist shower area. You quickly sense the difference if you step outside. Away from the moisture, net evaporation takes place quickly and you feel chilly. But, if you remain in the shower stall, even with the water turned off, the warming effect of condensation counteracts the cooling effect of evaporation. If as much moisture condenses as evaporates, you feel no change in body temperature. If condensation exceeds evaporation, you are warmed. If evaporation exceeds condensation, you are cooled. So now you know why you can dry yourself with a towel much more comfortably if you remain in the shower stall. To dry yourself thoroughly, you can finish the job in a less moist area.

4) Spend a July afternoon in dry Tucson or Phoenix where evaporation is appreciably greater than condensation. The result of this pronounced evaporation is a much cooler feeling than you would experience in a same-temperature July afternoon in New York City or New Orleans. In these humid locations, condensation noticeably counteracts evaporation, and you feel the warming effect as vapor in the air condenses on your skin. You are literally being bombarded by the impact of H2O molecules in the air slamming into you. Put more mildly, you are warmed by the condensation of vapor in the air upon your skin.

 

Condensation is the phase change of water __________ into a _________. During the condensation on process, water __________ lose the 600 cal/gm of latent heat that were added during the evaporation process. When latent heat is ____(called the @latent heat of fusion@), it is converted into sensible heat which warms the surrounding air. Condensation takes place in the presence of condensation nuclei and when the air is nearly saturated.

Water vapor is darting around so fast in the air that the molecules tend to bounce off one another without bonding. Even if a few pure water molecules were to _____ and bind together, the -------- TENSION CREATED BY SUCH A TINY SPHERE IS SO GREAT THAT IT IS EXTREMELY DIFFICULT FOR ADDITIONAL WATER MOLECULES TO BECOME INCORPORATED INTO THE MASS.

 

Text 7. Wireline channels

(from Fundamentals of Electrical Engineering I by Don Johnson, the Connexions Project, Rice University, Houston TX, 2002)

1) Wireline channels were the first used for electrical communications in the mid-nineteenth century for the telegraph. Here, the channel is one of several wires connecting transmitter to receiver. The transmitter simply creates a voltage related to the message signal and applies it to the wire(s). We must have a circuit -a closed path -that supports current flow. In the case of single-wire communications, the earth is used as the current's return path. In fact, the term ‘ ground’ for the reference node in circuits originated in single-wire telegraphs. You can imagine that the earth's electrical characteristics are highly variable, and they are. Single-wire metallic channels cannot support high-quality signal transmission having a bandwidth beyond a few hundred Hertz over any appreciable distance.

2) Consequently, most wireline channels today essentially consist of pairs of conducting wires Figure 6.1, and the transmitter applies a message-related voltage across the pair. How these pairs of wires are physically configured greatly affects their transmission characteristics.One example is ‘ twisted pair’, wherein the wires are wrapped about each other. Telephone cables are one example of a twisted pair channel. Another is ‘ coaxial cable’, where a concentric conductor surrounds a central wire with a dielectric material in between. Coaxial cable, fondly called "co-ax" by engineers, is what Ethernet uses as its channel. In either case, wireline channels form a dedicated circuit between transmitter and receiver.

3) As we shall find subsequently, several transmissions can share the circuit by amplitude modulation techniques; commercial cable TV is an example. These information-carrying circuits are designed so that interference from nearby electromagnetic sources is minimized. Thus, by the time signals arrive at the receiver, they are relatively interference- and noise-free.

4) Both twisted pair and co-ax are examples of ‘ transmission lines’, which all have the circuit model shown in Figure 6.2 for an infinitesimally small length. This circuit model arises from solving Maxwell's equations for the particular transmission line geometry.

5) The so-called distributed parameter model for two-wire cables has the depicted circuit model structure. Element values depend on geometry and the properties of materials used to construct the transmission line. The series resistance comes from the conductor used in the wires and from the conductor's geometry. The inductance and the capacitance derive from transmission line geometry, and the parallel conductance from the medium between the wire pair. Note that all the circuit elements have values expressed by the product of a constant times a length.