## Path Independence and Thermodyanamics

Earlier in the year we said that the work necessary for hiking up the slope of Rampina Mountain vs. climbing straight up the cliff route would be the same, independent of the path taken.

This statement is true if you disregard friction and other factors, but one path has a greater length and more friction will be experienced (probably).

May approaches in physics are approximations, but they can be fairly accurate up to a certain point.

If you climb a rope, the friction between your hands and the rope or your gloves and the rope would be unique.  The friction between your shoes and the ground could vary on shoe type, etc.

Or the ground could be icy……

Thus the work is not really path independent.

Even more so, thermodynamics is not path independent-

While throwing a marble up and watching it come down is symmetrical in motion, the rewinding of a camera of a thermodynamic reaction would definitely not be the same as playing it from the beginning (at least in all likeliness).

## Heat Flow

Heat naturally flows from warmer to cooler.  Things tend towards equilibrium.

Therefore heat vents are most efficiently placed on the floors of rooms so the heat might rise up throughout the room.

If the vents were on the ceiling, then all the heat would stay towards the top of the room.

And fans are then placed on the ceiling to circulate the air around more efficiently.

All this works according to the formula H=K*L/A(TH-TC) where K is the coefficient of thermal cooling for a substance.

## Latent Heat of Fusion | Latent Heat of Evaporation

If you add heat to some substance it will not necessarily change temperature.

Energy also can work towards producing a phase change, such as from solid to liquid or liquid to gas.

Water might heat up and change temperature or some portion of it might turn instantly to steam, leaving the rest of the water at the same temperature.

The “latent heat of fusion” and “latent heat of evaporation” will vary for different materials and can be used to calculate the energy necessary for these changes.

## What is Heat? And Heat Transfer

The term heat refers to the flow of energy.

If you drank a cool drink, it would only cool you down the difference in temperature for that amount you drink.

The liquid is brought into your system and therefore will warm up to your body temperature, while your body correspondingly cools down a little bit.

Different materials have different specific heat capacities so something like lead will heat up much faster than water.

The lead will also cool down faster while the water retains heat for much longer, this is partially related to hydrogen bonding in water.

## How a Thermostat Works, Thermal Expansion Coefficients

A good thermostat will accurately measure the environment while simultaneously not greatly changing its surroundings.

The basic construct that that makes a non-digital thermostat work is that a bimetallic strip has two layers of different metals.

The two coefficients of thermal expansion will be different, so because the two layers are connected, the thermostat will bend in a certain way according to temperature.

For instance aluminum will expand faster than brass.

Another element, quartz has an especially low coefficient of thermal expansion and is thus used in clocks to keep time since it contracts and expands with regularity only a small amount.

## Speed of Light and Relative Speed

If Spaceman Spiff attaches a flashlight to the front of his spacecraft the light is still going to travel at the speed of light c.

Likewise if he attaches a loudspeaker to his ship in order to yell at aliens, those waves will travel at the speed of sound.

While a military plane going mach five (five times the speed of sound) could hit its own bullets, both sound and light travel at speeds independent of the source.

The plane that attains a speed of mach five will also undergo the most stress as it passes mach one since it experiences the constructive interference of the entire cone of sound at that point.

## Decibels, Loudness

From woodleywonderworks on flickr

When someone returns from a heavy metal concert they don’t usually comment loudly about how many Watts per meter squared they experienced.

Decibels might make sense.  People tend to know that 120 Decibels is a lot.

This system has been devised and units of decibels measure perceived loudness.

It increases on a logarithmic scale, so something that seems twice as loud really has 10 times the intensity.

Position also can vary the perception of sound such as when a noise emitter comes nearer to you the frequency seems greater and the pitch higher (Doppler Effect).

## Wave Interaction, Beats, Destructive Interference

When waves come into contact with each other they can interact together to increase or decrease amplitude.

If two sound waves are slightly off in frequency you can hear the peaks where the waves add together (constructive interference), called “beats.”

If two identical waves are off by a phase angle of pi then there will be complete destructive interference, meaning that all the energy will be cancelled while they are in contact.

Sound cancelling headphones take advantage of this property by creating waves that cancel background noise.

## Wave Mediums, Bulk Modulus

Waves must be distinguished as to what medium they are traveling through, if you want to make any sense of data.

Sound will travel at a certain rate in air and another in water, and these rates can be quite different.

Materials have something called the bulk modulus which has to do with elasticity and the ease with which waves propagate through a particular substance.

Lightning goes through the air at about 1/5 mile/sec, and therefore you can count the seconds between the flash and the sound to determine how far away the lightning struck.

Temperature also affects the bulk modulus, so it should be taken into account for better precision.

## Vectors, components, sine and cosine in power series

Back in algebra II or so you probably started going over vectors.

To start off, you could describe a vector using an angle (like that on a compass) and a magnitude or as two components (i and j).

Later on, in three dimensions you could use i, j, and k components to describe a vector.

In earlier grades, teachers taught cosines and sines only in their relations to triangles, but it turns out that the sine and cosine functions can describe any function (this is related to power series).

Furthermore, a combination of sines and cosines can act as the basis of n-dimensional space.

Thus they prove to be useful far beyond describing triangles.