UGC NET Paper 1 Mathematical Reasoning & Aptitude.pdf
Thermodynamics
1. Internal Energy and the First Law of Thermodynamics
The total energy of a system is defined as the internal energy,
symbolized as U.
The internal energy is composed of energy from different
sources, like chemical, electronic, nuclear, and kinetic energies
The absolute total internal energy of any system cannot be
known. But all systems have some total energy U
An isolated system does not allow for passage of matter or
energy into or out of the system. (A closed system, on the other
hand, allows for passage of energy but not matter.)
If energy cannot move in or out, then the total energy U of the
system does not change. The explicit statement of this is considered
the first law of thermodynamics
For an isolated system, the total energy of the system remains
constant.
For an isolated system, U = 0
2. In all investigations of energy changes in systems, it has been found that
when the total energy of a system changes, the energy change goes into
either work or heat, nothing else. Mathematically, this is written as
3.
4. Kinetic theory shows that the molar translational energy of a
monatomic ideal gas is
The translational energy is independent of pressure or molar mass for
a monatomic ideal gas so that
RT
2
3
RTU
2
3
Gases like Ar, Ne, and He have
constant-pressure heat capacities
around 20.8 J/mol . K, which is not
surprising. The lighter inert gases are
good approximations of ideal gases.
5.
6. Monatomic ideal gases have a temperature-invariant heat capacity; real gases do
not. Most attempts to express the heat capacity of real gases use a power series, in
either of the two following forms:
where a, b, and c are experimentally determined constants
The change in enthalpy with temperature at constant pressure is then given by
7. JOULE THOMSON EXPANSION
A gas flowing along an insulated pipe through a porous plate that
separates two regions of different constant pressures may be heated
up or cooled down. This is shown in Fig
where . P1 > P2, To push one mole of gas through the porous plate, work
amounting P1V1 to has to be done on one mole of the gas by the piston on the
left. Work amounting P2V2 to is done on the surroundings by one mole of gas
pushing the piston on the right, and so the net work on the gas is
8. Thus we see that there is no change in the enthalpy of the gas in a Joule–Thomson
expansion.
9. ADIABATIC PROCESSES WITH GASES
Now we consider the compression and expansion of gases in isolated systems. No heat
is gained or lost by the gas, so the process is adiabatic (dq = 0 )and the first law
becomes simply
dU = dq + dw dq = 0
dU = dw
10.
11.
12. The Chemical Potential and Partial Molar Quantities
In thermodynamics, chemical potential, also known as partial molar free energy, is a
form of potential energy that can be absorbed or released during a chemical reaction
or phase transition.
The chemical potential of a species in a mixture is defined as the rate of change of
a free energy of a thermodynamic system with respect to the change in the number of
atoms or molecules of the species that are added to the system
The chemical potential of a substance, m, is defined as the change in the Gibbs energy with
respect to amount at constant temperature and pressure:
14. Heat Capacity of Solid
At low temperatures, most matter is solid, and the best type of solid sample to study is a
crystal. Studies of crystals showed some intriguing thermodynamic behavior. For instance,
in the measurement of entropy it was found that absolute entropy approached zero as the
temperature approached absolute zero. This is experimental verification of the third law of
thermodynamics. But a measurement of the heat capacity of the solid showed something
interesting:
The heat capacity of the solid approached zero
as the temperature approached absolute zero,
also. But for virtually all crystalline solids, the
heat-capacity-versus-temperature plot took on
a similar shape at low temperatures
Experimentally it was found that the constant-
volume heat capacity CV was directly related
to T3
15. Einstein proposed to understand the motions of the atoms in the crystal using Planck’s idea of
quantized energy. A crystal is composed of N atoms, say. These N atoms can vibrate within their
crystal lattice in the x, the y, or the z direction, giving a total of 3N possible vibrational motions.
Einstein assumed that the frequencies of the vibrations were the same, some frequency labeled
vE, or the Einstein frequency.
If this were the case, and we are only considering vibration-type motions of the atoms in the
crystal, then the heat capacity of the crystal can be determined by applying the vibrational part
only of the heat capacity from the vibrational partition function:
This is not the T3-dependence, as experimental
measurements suggest.
16. Peter Debye, a Dutch physical chemist after whom the Debye-Huckel theory is
partly named expanded on Einstein’s work
Rather than assume that all atoms in a crystal had the same vibrational frequency (as Einstein
had presumed), Debye suggested that the possible vibrational motions of the atoms in a
crystal could have any frequency from zero to a certain maximum. That is, he suggested that
atoms could have a range, or distribution, of frequencies
Debye deduced that the equation for the distribution of frequencies,
symbolized by g(), is
17. Einstein debye
Both Einstein’s and Debye’s treatment of crystals are approximations
in the sense that they assume some ideal behaviour. Like real gases,
real solids do not behave ideally
18. Entropy and the Second Law of
Thermodynamics
Definition of the change in entropy S when an
amount of heat Q is added:
Another statement of the second law of
thermodynamics:
The total entropy of an isolated system never
decreases.
19. for any spontaneous (that is, irreversible) change, the entropy of
the universe increases.
the second law of thermodynamics can be expressed in terms of the
system and surroundings interacting
