It presents PT diagram,PV diagram and constant volume,constant pressure,constant temperature relation and adiabatic process.

1. PVT Behaviour

2. P-V-T Behavior of Pure Substances
PT Diagram
• A typical P-T diagram
showing the relationship
between pressure and
temperature of a pure
substance is shown
below:

3. P-T Diagram
• The three lines 1-2, 2-3
and 2-C display
conditions of P and T at
which two phases may
co-exist in equilibrium,
and are boundaries for
the single-phase regions
of solid, liquid and
vapor (gas).

4. Graph Explanation
• Line 1-2 is known as the sublimation curve,
and it separates the solid from the gas regions.
• Line 2-3 is known as the fusion curve, and it
separates the solid and liquid regions.
• Line 2-C is known as the vaporization curve,
and it separates the liquid and the gas regions.
All three lines meet at Point 2, known as the
Triple Point. This is a point where all 3 phases
can co-exist in equilibrium.

5. Critical Pressure and Critical
Temperature
• The pressure and temperature corresponding to
this point(Critical Point) are known as the critical
pressure PC and critical temperature TC
respectively. These are the highest pressure and
temperature at which a pure substance can exist in
vapor-liquid equilibrium.
• The shaded area shows the area existing at
pressure and temperature greater than P and T.
This region is called the fluid region.

6. Explanation
• The gas region is sometimes divided into two
parts, as indicated by the dotted vertical line
through temperature TC.
• A vapor region is the region to the left of this line
and represent a gas that can be condensed either
by compression at constant temperature or by
cooling at constant pressure.
• The region everywhere to the right of this line,
including the fluid region, is termed supercritical.

7. P-V Diagram for Pure Substance
• The P-T Diagram does not provide any
information about volume.
• It merely displays the phase boundaries on as a
function of pressure and temperature.
• On the P-V Diagram, the triple point appears
as a horizontal line, where all 3 phases co-exist
at a single temperature and pressure.

8. P-V Diagram

9. P-V Diagram
• Isotherms are lines of
constant temperature
and these are
superimposed on the P-
V Diagram as shown in
the Figure.

10. Explanation
• Point C is the critical point. VC is the critical
volume at this point.
• The isotherm labeled T > TC does not cross a
phase boundary.
• The lines labeled T1 and T2 are isotherms for
subcritical temperatures, and they consist of 3
segments.

11. • The horizontal segment of each isotherm
represents all possible mixtures of liquid and
vapour in equilibrium, ranging from 100%
liquid at the left end (curve B-C) to 100%
vapour at the right end (curve D-C).
• Curve B-C represents saturated liquid at their
boiling points, and curve D-C represent
saturated vapours at their condensation points.

12. PV Diagram
• Subcooled liquid and superheated vapour
regions lie to the left and right, respectively.
• Subcooled liquid exists at temperatures below
the boiling point for the given pressure.
• Superheated vapour exists at temperatures
above the boiling point for the given pressure

13. PV Diagram (Continue)
• Isotherms in the subcooled liquid region are
very steep, because liquid volumes change
little with large changes in pressure.
• The horizontal segments of the isotherms in
the 2-phase region become progressively
shorter at higher temperatures, being
ultimately reduced to a point at C, the critical
point.

14. PROCESSES INVOLVING IDEAL GASES
CONSTANT VOLUME AND CONSTANT
PRESSURE
1. CONSTANT VOLUME PROCESSES:
• An isochoric process, also called a constant-
volume process, an isovolumetric process, or an
isometric process, is a thermodynamic process
during which the volume of the closed system
undergoing such a process remains constant.
• The noun isochor and the adjective isochoric are
derived from the Greek words isos meaning
"equal", and choros meaning "space”.

15. For a constant volume process, the addition or
removal of heat will lead to a change in the
temperature and pressure of the gas, as shown on the
two graphs above

16. Applying the first law of thermodynamics to the process
dU = dQ - dW
Replacing dW with the reversible work
dU = dQ - PdV
since the volume is constant dV = 0 and
dU = dQ
using the definition of the specific heat at constant volume
𝐶 𝑉 =
𝑑𝑄
𝑑𝑇
so, dU=𝐶𝑣dT=dQ

17. 2.CONSTANT PRESSURE PROCESS:
• An isobaric process is a thermodynamic process in
which the pressure stays constant: ΔP = 0.
• The term derives from the Greek iso- (equal) and
baros (weight). The heat transferred to the system
does work, but also changes the internal energy of
the system

19. Applying the first law of thermodynamics to the process
dU = dQ - dW
Replacing dW with the reversible work and Using the
definition of specific heat capacity at constant pressure,
𝑐 𝑃=
𝑑𝑄
𝑑𝑇
dU = 𝐶 𝑝 dT – PdV
then,
dU+PdV= 𝐶 𝑃DT
dH=𝐶 𝑝 dT

20. 3. CONSTANT TEMPERATURE PROCESS:
• This is a process where the temperature of the
system is kept constant.
ΔU = 0, ΔT = 0,
• When volume increases, the pressure will
decrease, and vice versa.
ΔT = 0 then: ΔV ↑and P ↓ OR ΔV↓ and P
↑ (inverse relationship)
• As an example, gas molecules are sealed up in a
container but an object on top of the container
(such as a piston) pushes down on the container
in a very slow fashion that there is not enough to
change its temperature.

21. Figure: Isothermal Process in Graphical Form

22.  To derive the equation for an isothermal
process we must first write out the first law of
thermodynamics:
 Rearranging this equation a bit we get:
 Since ΔT = 0. Therefore we are only left with
work.
 In order to get to the next step we need to use
some calculus:

23. • The equation for an isothermal process.

24. • 4. ADIABATIC PROCESSES:-
• For an adiabatic free expansion of an ideal gas, the gas
is contained in an insulated container and then allowed
to expand in a vacuum. Because there is no external
pressure for the gas to expand against, the work done
by or on the system is zero.
• Since this process does not involve any heat transfer or
work, the First Law of Thermodynamics then implies
that the net internal energy change of the system is
zero.
• For an ideal gas, the temperature remains constant
because the internal energy only depends on
temperature in that case. Since at constant temperature,
the entropy is proportional to the volume, the entropy
increases in this case, therefore this process is
irreversible.

25. • Derivation of P-V relation for adiabatic
heating and cooling.

26. • Now substitute equations (2) and (4) into equation (1) to
obtain
• factorize :
• and divide both sides by PV:
• After integrating the left and right sides from to V and
from to P and changing the sides respectively,

27. • Exponentiate both sides, and
substitute with , the heat capacity ratio.
and eliminate the negative sign to obtain
• Therefore,
• And

28. • Derivation of T-V relation for adiabatic heating
and cooling:-
• Substituting the ideal gas law into the above,
we obtain
which simplifies to

29. • THANK YOU