PVT Behaviour

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:

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).

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.

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.

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.

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.

P-V Diagram

P-V Diagram

• Isotherms are lines of

constant temperature

and these are

superimposed on the P-

V Diagram as shown in

the Figure.

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.

• 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.

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

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.

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”.

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

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

𝐶𝑉 =𝑑𝑄

𝑑𝑇so, dU=𝐶𝑣dT=dQ

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

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,

𝑐𝑃=𝑑𝑄

𝑑𝑇

dU = 𝐶𝑝 dT – PdV

then,

dU+PdV= 𝐶𝑃DT

dH=𝐶𝑝 dT

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.

Figure: Isothermal Process in Graphical Form

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:

• The equation for an isothermal process.

• 4. ADIABATIC PROCESSES:-

• For an adiabatic free expansion of an ideal gas, the gasis contained in an insulated container and then allowedto expand in a vacuum. Because there is no externalpressure for the gas to expand against, the work doneby or on the system is zero.

• Since this process does not involve any heat transfer orwork, the First Law of Thermodynamics then impliesthat the net internal energy change of the system iszero.

• For an ideal gas, the temperature remains constantbecause the internal energy only depends ontemperature in that case. Since at constant temperature,the entropy is proportional to the volume, the entropyincreases in this case, therefore this process isirreversible.

• Derivation of P-V relation for adiabatic

heating and cooling.

• 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,

• Exponentiate both sides, and

substitute with , the heat capacity ratio.

and eliminate the negative sign to obtain

• Therefore,

• And

• Derivation of T-V relation for adiabatic heating

and cooling:-

• Substituting the ideal gas law into the above,

we obtain

which simplifies to

• THANK YOU