Third law of thermodynamics
The third law of
thermodynamics was formulated by Walther Nernst. This law is concerned about
the limiting behavior of the system as the system approaches absolute zero. Regarding
the properties of the closed system in thermodynamic equilibrium, the third law
of thermodynamics states:
“The entropy of a system approaches a constant value as
its temperature approaches absolute zero.”
Before going into deep concepts, we need to explain some
terms which are necessary for a better understanding of the topic. The main
terms which will use in this topic are
Thermodynamics equilibrium: If the object is at
constant temperature and maintains it then it is said to be thermal
equilibrium. For example, when a higher temperature object is in contact with a
lower temperature, the object will transfer heat to the lower temperature
object. Then, the object will approach the same temperature, they will then
maintain a constant temperature. They are then said to be in thermal
equilibrium
Closed system: In a closed system energy can be
transferred but matter cannot be transferred across the boundary. e.g., The
compression of gas molecules in piston-cylinder is an example of a closed
system
Entropy: It is the property of thermodynamics. It is
also a state function. Entropy is defined as a measure of the disorder
of a system. It is a physical property associated with uncertainty,
randomness. It is designated by s. Its unit
is call/ kola.
Absolute zero: Absolute zero is the temperature of an
object which is taken as zero on the scale. Absolute temperature is a state
where the system is in a lower (minimum) energy state. As molecule approaches
this state their movements drop towards zero. The kinetic energy of the
molecules becomes negligible. The absolute temperature scale is kelvin.
0
k (absolute temperature) = -273.15 Celsius
Explanation:
The unique microstate state (ground state) with minimum
energy, in such case the entropy at absolute temperature will be absolutely
zero. If the system does not have this state then, there may remain such finite
entropy as the system bought to the low temperature. For example, in glassy
type order, this would happen.
Example:
The entropy of perfect crystal lattice ofc pure substance
approaches as zero as the temperature zero. The alignment of a perfect crystal has
no disorder and ambiguity on its orientation of each part of the crystal.
Application:
The application of the third law of thermodynamics is it
provides an absolute reference point for the determination of entropy at any
other temperature.
The important application of the third law of thermodynamics
is that it helps in the calculation of the absolute entropy of a substance at
any temperature. This can be measure by heat capacity measurements of the
substance.
For any solid:
Let S0 be the entropy at 0k and S be the entropy at TK, then
Delta= S-S0= INTEGRAL
According to the
third law of thermodynamics, s0 = 0 at 0K
S=
The value of this
integral can be obtained by plotting the graph of Cp/T Versus T and then
finding the area of this curve from 0 to T. the simplified expression for the
absolute entropy of a solid at temperature T is as follows
Here CP is the heat capacity of the substance at constant
pressure and this value is assumed to be constant in the range of 0 to TK.
Mathematical calculation:
The entropy of the closed system is determined relative to the
zero points. Mathematically, the entropy of this system at absolute temperature
is the natural log of the number of ground states and Boltzmann’s constant.
S-S0=Kulpi
S= is the entropy of the system
S0=is the initial entropy
KB =denotes the Boltzmann’s constant
KB=3.8*10-23JK-1
Pi = refers to the total number of microstates that are consistent
with the system macroscopic configuration.
For the perfect crystal lattice:
The entropy of a perfect gas crystal is zero at its ground
state is unique because ln (1) =0.
S-S0= Kulpi= KB ln= 0
The initial value is zero
S-S0=S-0=0
S=0
A system with non-zero entropy at absolute temperature:
A system that does
not have a unique ground state has non-zero entropy at absolute zero. These are
ones whose net spin is a half-integer, for which time-reversal symmetry gives
two degenerate ground states. For such a system, the entropy at zero temperature
is at least KB*ln (2) which is negligible on a macroscopic scale.
For glasses and solid solutions: The glasses and
solid solutions retain large entropy at 0k because they are large collections
of nearly denigrate states, in which they become trapped out of equilibrium.
For example, ice
For ferromagnetic and diamagnetic material:
The entropy at
absolute zero is zero when the magnetic moment of the perfectly ordered crystal
must themselves be perfectly ordered. And ferromagnetic and diamagnetic satisfy
this condition. Reason: Ferromagnetic have zero entropy at zero temperature
because the spins of the unpaired election electrons are all aligned and this
gives a ground-state spin degeneracy.
For perfectly ordered structure:
The magnetic moments of a perfectly ordered crystal must themselves
be perfectly ordered.
Why absolute
temperature is impossible to achieve?
The third law states are equivalent to the statement that;
It is impossible to reduce the temperature of any closed system to zero
temperature in a finite number of finite operations, no matter how idealized
the system.
Explanation:
For the isentropic process, the temperature can be reduced
by changing the parameter for supposing X from X2 to X1. An infinite number of
steps are required to cool the substance to zero kelvin.
Graph
From the graph, it is illustrated that the lower the temperature,
the greater number of steps required to cool the substance further. As the
temperature approaches zero kelvin, the number of steps required to cool the substance
approaches infinity.
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