09-05-2012, 04:45 PM
IRREVERSIBLE THERMODYNAMICS
IRREVERSIBLE THERMODYNAMICS.doc (Size: 7.07 MB / Downloads: 148)
Phenomenological Laws
A large number of phenomenological laws exists, which describe the irreversible processes in the form of proportionalities
For example, Fourier’s law between heat flow and temperature gradient
Fourier’s equation for one-dimensional conduction of heat along a bar is
(dQ / dt) = - kA (dT / dX)
Where Q = Quantity of energy, (heat)
T = Temperature
A = Area of cross section
X = length
k = Thermal conductivity
Ohm’s law relating electrical current and the potential gradient
Ohm’s Law for flow of electricity along a wire, which is also one-dimensional, is
I = (dql / dt) = - λ A (de / dl)
Where I = Current
ql = Charge (coulomb)
e = Potential difference (voltage)
A = Area of cross section of wire
l = length
λ = Electrical conductivity
Ficks Law relating flow of matter and its concentration gradient
Ficks law for the diffusion due to a concentration gradient is, in one dimension
dni / dt = - k (dCi / dl)
where ni = Amount of substance i
Ci = Concentration of component i
k = Diffusion coefficient
Newton’s law between shearing force and velocity gradient
The chemical reaction law between reaction rate and chemical potential
Generalized forces and Fluxes
The causes which are responsible to the occurrence of these irreversible phenomena, such as the temperature gradient, potential gradient, concentration gradient and chemical affinity are called the generalized forces, and is denoted as Xi ( i = 1, 2, 3 …n)
The irreversible phenomena, such as heat flow, electrical flow, diffusion, chemical reaction rate,etc.,caused by the forces are called fluxes, symbolized by Ji (I=1,2,. n)
A thermodynamic force may be defined as a quantity which measures the extent to which the system is displaced from equilibrium
The above equations relate the flow of one quantity to a difference in potential: hence, there is a flow term and a force term as suggested by the equation J = LX
Where J is the thermodynamic velocity or flow and X is the thermodynamic force
L is a coefficient independent of X and J and is a scalar in form, While both J and X are vector quantities
It will be shown that although the above equations appear to have the correct form, they are not the most appropriate relationships for some problems
The above equations also define the relation between individual fluxes and potentials, whereas in many situations the effects can be coupled
When two or more of these phenomena occur simultaneously, they interfere and give rise to new effects known as cross-coupling phenomena
Cross-Coupling Phenomena
The examples of such cross-coupling phenomena are:
o The two reciprocal phenomena of thermoelectricity arising from the interference of heat conduction and electrical conduction, viz See beck effect and Peltier effect (evaluation or absorption of heat at a junction due to flow of electrical current)
o The coupling of diffusion and heat conduction giving rise to thermal diffusion, called the Soret effect (concentration gradient formed as a result of a temperature gradient) and its inverse phenomenon, the Dufour effect (temperature difference arising when a concentration gradient exists)
Seebeck Effect
Consider two wires made from different metals joined at both the ends (junctions), forming a closed circuit
Ordinarily nothing will happen. But one end is heated, something interesting happens: A current flows continuously in the circuit, as shown in Figure 10.22
This is called the Seebeck effect, in honor of Thomas Seebeck, who made this discovery in 1821
The circuit which incorporates both thermal and electrical effects is called a thermoelectric circuit, and a device that operates on this circuit is called a thermoelectric device
The Seebeck effect has two major applications: temperature measurement and power generation
When the thermoelectric circuit is broken, as shown in figure 10.23, the current ceases to flow, and we can measure the driving force (the electromotive force) or the voltage generated in the circuit by a voltmeter
The voltage generated is a function of the temperature difference and the materials of the two wires used