Department of Mechanical Engineering ME 322 – Mechanical Engineering Thermodynamics
Lecture 6
• Thermodynamic Diagrams
• Phase Change
Thermodynamic Diagrams
The P-v-T Surface To view the T-v diagram look at the top view of
Thermodynamic Diagrams
The State Postulate
Two independent, intensive properties fix the thermodynamic state of a simple substance
Typical Phase
Diagram This state is fixed by T and P which are independent in the single phase. Once the state is identified, all thermodynamic
properties of the state are known.
, T P 1 / , p v v u h s c c ρ = Defines
The State Postulate
Two independent, intensive properties fix the thermodynamic state of a simple substance
Typical Phase
Diagram This state on the p-T plot is unclear. What phase is the substance in? It’s right on the liquid-vapor line.
, T P 1 / , v u h s c c ρ = Defines
Phase Change
What is we put a sealed container with a moving piston on the stove? The other side of
the piston is exposed to
atmospheric pressure Start with liquid at T = 72 °F
Add heat what happens?
Phase Change
What about other pressures?
T 14.696 psia atm P = P = atm P > P atm P > P atm P < P 72 F T = ° 212 F T = °
What is a Gas? Superheated Vapor?
While Superheated Vapor and Gas may behave similarly, they are defined differently.
• Superheated Vapor
• To the right of the Saturated Vapor line
• Temperature is below the Critical Temperature • Gas
• Temperature is above Critical Temperature • Pressure is below the Critical Pressure
• SuperCritical
T-v Diagram
T critical point L c T c P V G SC L + VP-v Diagram
P critical point L c T c P V G SC L + VThermodynamic Nomenclature
Phase Thermodynamic Name
Liquid Compressed liquid Vapor Superheated vapor
Liquid + Vapor Wet, Saturated, or 2-Phase Mixture
Gas Gas
Supercritical Supercritical
Saturation Property Nomenclature
Saturated liquid properties are signified with a subscript f Saturated vapor properties are signified with a subscript g Saturated solid properties are signified with a subscript i
Quality – A New Property
p v v f v vgp,T are NOT independent in the wet region. However,
p,v and T,v are independent. But, what if you are trying to find v? To do this, I need another independent,
intensive property to fix the state of a saturated mixture. The property we need is the
Quality – A New Property
Consider the total volume of a wet mixture …
f g f g m m v v v m m = + g V f V f g V = V + V f g V V V v m m m = = + f f g g m v m v v = + Define ... x mg m = = quality Therefore ... mf 1 x m = − Substituting ... v =
(
1− x v)
f + xvg ←Quality – A New Property
(
)
(
)
(
)
(
)
1 1 1 1 f g f fg f g f fg f g f fg v x v xv v xv u x u xu u xu h x h xh h xh s x s xs s xs = − + = + = − + = + = − + = + = − + = +Quality expressions are valid for other internal energy, enthalpy, and entropy too!
A little algebra ...
(
1)
f g f f g f(
g f)
f fg fg g f v x v xv v xv xv v x v v v xv v v v = − + = − + = + − = +Department of Mechanical Engineering
ME 322 – Mechanical Engineering Thermodynamics
Property Models
The Incompressible Substance Model
The Ideal Gas Model
Department of Mechanical Engineering
ME 322 – Mechanical Engineering Thermodynamics
The Incompressible Substance
Model
( )
v
u
u T
=
=
constant
Liquids
and
Solids
The Incompressible Substance Model
As seen in the reading (Section 3.9.1),
v du = c dT
If we know the value of c (or the variation of c with T), the
above equation, du = cdT can be integrated between any two states to determine the change in internal energy. Once the change in internal energy is known, the change in enthalpy It can also be shown (see Section 3.9.1) that,
p v p h du c c c T dT ∂ = = = ≡ ∂ (specific heat)
Department of Mechanical Engineering
ME 322 – Mechanical Engineering Thermodynamics
The Ideal Gas Model
( )
pv
RT
u
u T
=
=
Gases
T
>> T
cand
The Ideal Gas Model
As seen in the reading (Section 3.9.2),
v du = c dT
Since we are dealing with an ideal gas, pv = RT. Therefore,
( )
h = +u pv → h = +u RT → h = h T
This leads to the following conclusion (section 3.9.2),
p dh = c dT
The Ideal Gas Model
v p p v
du = c dT dh = c dT c −c = R
Significance:
These equations allow us to determine internal energy and enthalpy changes for ideal gases. In order to integrate the
du and dh equations, we need to determine one of the specific heats (the other can be found with the third equation).
With ideal gases, the specific heat dependence on
temperature may be stronger compared to incompressible substances. Exceptions: The heat capacities are constant
Department of Mechanical Engineering
ME 322 – Mechanical Engineering Thermodynamics
