Thermal+Physics

Topics

 * Energy
 * Convection, Conduction and Radiation
 * Thermal Energy Flow
 * The Gas Laws (and model gases).

Energy
Energy is an abstract concept, sometimes referred to as an accounting system. It is that which is conserved in interactions. It is the ability to do mechanical work.

There are many times of energy. One summary of them (with a mnemonic) is:


 * P**lease **H**elp **mE** **C**onserve **E**nergy, **K**indly **S**witch-off **L**ights **N**ow


 * P**otential (gravitational)
 * H**eat
 * E**lectric (and **m**agnetic)
 * C**hemical
 * E**lastic (strain)
 * K**indly
 * S**ound
 * L**ight
 * N**uclear

Or: **M**ost (magnetic) **K**ids (Kinetic) **H**ate (Heat) **L**earning (Light) **G.C.S.E.** (Gravitational.Chemical.Sound.Elastic) **E**nergy (Electric) **N**ames (Nuclear)

Convection, Conduction and Radiation
Does a flame point upwards in a space station - answered by an astronaut:

[|Astronaut explains flames in free fall]

Extension activities:
Make a coke can stirling engine: []

Ideal Gases
Note: The absolute scale of temperature (where absolute means that zero really is zero - you can't go lower) is called the Kelvin scale. One degree of change in temperature is the same in Celsius or kelvin, but 0 kelvin is equal to approximately -273 o C. Hence ice freezes at 273 K (0 o C). To convert Celsius to Kelvin, simply add 273. The symbol T refers to absolute temperature.

Experimentation can show the following three **gas laws** are valid for all gases in most circumstances:

pV = constant (aka Boyle's law). p/T = constant (aka Charles' law) V/T = constant (aka Pressure law)



These are valid for real gases as long as the gas is not under high pressure nor close to its boiling point (i.e. in situations where the gas particles are unusually close together, so that intermolecular forces will have a material effect).

An **ideal gas** is one that obeys all three gas laws at all values of temperature, pressure and volume. For an ideal gas the three gas laws can be combined into the **equation of state** for an ideal gas:

(1) pV = nRT, where

n = number of moles R is molar gas constant (approx 8.3 J mol -1 K -1 (or m 2 kg s -2 mol -1 K -1 ))

//Link to Chemistry -// in chemistry students may be taught that the volume of a gas (in cm 3 ) is equal to the number of moles times 24 000. This follows from equation (1) above, taking R to be approximately 8, T to be standard temperature (approx 300 o K), p to be 100kPa (standard pressure), and V to be measured in cm 3, so that the RHS of the equation need to be multiplied by 10 6 (the multiplication factor to get from m 3 to cm 3 . Hence V=n*8*300*10 6 /10 000, and hence V = n * 24 000.


 * Kinetic Theory of Gases**

Making further assumptions about the ideal gas (such as: that the volume occupied by the particles is negligible, the intermolecular forces are negligible, and all collisions are elastic (no loss of k.e. - see below for a mnemonic for the assumptions)) then it can be shown that the pressure of an enclosed sample of ideal gas is proportional to the mean square speed :

(2) pV = 1/3 x Nm (or equivalently p = 1/3 r using total mass (Nm)/volume = density), where

N = total number of particles m = mass of each particle r = density

Assumptions of the kinetic theory of gases ("INVENT")

//The gas is made up of://


 * I || **I**dentical spheres of equal size, or which there are || The particles are homogeneous and symmetrical, so it doesn't matter which one you consider or which direction it is moving ||
 * N || a large **N**umber, and || The use of statistics is valid ||
 * V || their **V**olume is negligible compares to that of the vessel. || //The number of particles present in a given volume (density) does not effect the volume of the vessel (by taking up space).// ||
 * E || The collisions between the molecules or between the molecules and the walls of the vessel are **E**lastic, || Energy is conserved in collisions ||
 * N || No forces act between the molecules, and || The potential energy is zero; the only energy that needs to be considered is kinetic energy ||
 * T || the time taken for collisions to happen is negligible compared to the time between collisions. || The change of momentum is instantaneous. ||
 * T || the time taken for collisions to happen is negligible compared to the time between collisions. || The change of momentum is instantaneous. ||

Given that p is proportional to (for a given mass and volume), the p must also be proportional to 1/2m, the mean kinetic energy of the gas.

From (1) and (2) we can write:

nRT = 1/3 x Nm 3/2 x RT/N = 1/2 x m mean kinetic energy of an ideal gas = 3/2 x nRT/N

For one mole of gas (n=1) the number of particles (N) is equal to Avogadro's number N A, and R/N A is know as the Boltzman constant (k) which equals 1.38 x 10 23 J K -1 , so

mean kinetic energy of one mole of an ideal gas = 3/2 x kT.

Note: n/N = "no of moles" / "Number of particles"; and no. of moles = "no. of particles" / N A ; so n/N = ("no. of particles" / N A ) * (1 / "no. of particles") = 1/N A.