Introduction In Thermodynamic
( 2 )
5. Heat Transfer
When a hot surface surrounded by an area which is colder, energy in
the form of heat will be transferred from the hot surface to the cooler area.
The rate of this transfer is depended on the temperature difference and
the process will continue until both the surface and the surroundings are at the same temperature.
This process is called heat transfer and takes place by one or more of the following methods.
There are three ways of heat
transfer: Conduction, Convection and Radiation.
5.1 Conduction
Heat can be transmitted between two objects connection with each other, i.e. flow heat from one to the other.
There is movement of molecules
vibrating about its balanced position and grow this movement.
Conduction takes place in solids, liquids, and gases.
Solids offer the least resistance to transfer of heat by conduction.
Conduction requires physical contact between material through which the heat is transferred.
A materials temperature is related to the motion of the constituent molecules.
Microscopically, the radiation comes about because the oscillating ions and electrons in a warm solid are
accelerating electric changes.
Different substances radiate with different efficiencies, so substances that radiate better also absorb
incoming radiation better.
A perfect absorber is called a black
body (such perfection is not found in nature, but some things are close).
It was found experimentally that for a perfect black body at an even
temp., the radiant energy output in watts per square meter of surface went as the fourth power of the absolute temperature:
6. Ideal Gas
Gases are easier to deal with
theoretically.
In liquids and solids, the atoms are close enough to interact with one another and there results some
potential energy.
However, temperature does not indicate how much P.E.
Temperature is only an index of the mean K.E. per molecule or atom.
This requires the introduction of latent heat , ةنماكلا ةرارحلاwhich is a form of P.E.
In particular, we define an ideal gas to have the following properties:
1-There are no atomic interactions among the molecules or atoms
comprising the gas.
Therefore, there is no internal
potential energy resulting from such interactions, only kinetic energy.
2-The sizes of the atoms or molecules is extremely small compared with
their separations.
3-When the basic particles collide,
they do so in a perfectly elastic way.
What does this mean?. Historically, what we now call the equation of state for an ideal gas was
determined experimentally.
Consider measuring P ( pressure) and V (volume) for a gas at a constant temperature over a wide range for
these variables, to find a relationship between P and V.
The temperature must be expressed in Kelvins, and not any other
temperature system.
That is, T must be the absolute temperature.
This was first done by Boyle’s law:
Determined empirically by a series of isothermal processes:
P ~ 1/V.
This is a family of parabolas in the p-v plane.
Charles’ Law: Empirical result for a series of isobaric processes, V ~ T.
This is a family of straight lines in the v -T plane.
Gay-lussac law: For isochoric processes:
P ~ T.
This is also a family of straight lines in the P-T plane.
Combining these three relationships we get: PV = nRT, or PV = RT
Here R is a constant of
proportionality that must be
measured. It has been found to be the same value for all gases.
6.1 Kinetic Theory of gases
Molecular Model of an Ideal Gas
We will restrict this initial
description to monatomic gases
which we can treat as hard spheres which collide with each other and with the container walls.
For these gases the only form of
internal energy is the kinetic energy of translation (1/2) m v² of the
tiny spheres.
For diatomic or more complicated gases – like oxygen O2, water H2O, carbon monoxide CO2 – we will have to also consider the energy due to rotation and vibration.
The connection between the
microscopic motion of molecules (which we understand from
Newtonian Mechanics) and the macroscopic characteristics we
observe – such as pressure, volume, and temperature.
Consider a single monatomic gas atom of mass m, moving with
velocity v, having a component along the x-axis of vx.
this gas atom is confined to a cubic container with sides of length L.
If the atoms strike with the container wall.
The atom undergoes an elastic collision.
