The document discusses a thermodynamic mnemonic diagram used to remember thermodynamic properties and relationships. The square diagram has thermodynamic potentials clockwise on the sides and natural variables in the corners. Diagonal arrows indicate coefficients in differential expressions and their signs. Maxwell relations can be derived from this diagram by considering arrow directions. Common thermodynamic diagrams like temperature-entropy, pressure-volume, and Mollier diagrams are also discussed for visualizing thermodynamic cycles and processes. Residual properties are defined as the difference between actual and ideal properties.

1. Thermodynamic Square
A Mnemonic diagram to remember
Thermodynamic Diagrams
Graphical representation of thermodynamic properties
Residual Properties
Difference between the actual and the ideal

2. The differential expressions for the
thermodynamic potentials and Maxwell
relations can be remembered conveniently in
terms of a thermodynamic Mnemonic
diagram.
The diagram consists of a square with two
diagonal arrows pointing upwards and the
thermodynamic potentials in alphabetical
order clockwise on the sides as shown in
figure. The natural variables associated with
each potential are placed in the corners.

3. Diagonal arrows indicate the coefficients associated
with the natural variables in the differential expression
of the potential. The sign of the coefficient depends
on whether the arrow is:
dU = (sign)(coeff.) dS + (sign)(coeff.) dV
dU = (sign)TdS + (sign)PdV
dU = +TdS - PdV
 Pointing towards the natural variable (- ve)
 Away from the natural variable (+ ve).

4. 𝑑𝐴 = (𝑠𝑖𝑔𝑛)(𝑐𝑜𝑒𝑓𝑓𝑖𝑐𝑖𝑒𝑛𝑡)𝑑𝑇 + (𝑠𝑖𝑔𝑛)(𝑐𝑜𝑒𝑓𝑓𝑖𝑐𝑖𝑒𝑛𝑡)𝑑𝑉
𝑑𝐴 = − 𝑆𝑑𝑇 + − 𝑃𝑑𝑉
𝑑𝐴 = −𝑆𝑑𝑇 − 𝑃𝑑𝑉
Similarly:
𝑑𝐺 = −𝑆𝑑𝑇 + 𝑉𝑑P
𝑑𝐻 = 𝑉𝑑𝑃 + 𝑇𝑑𝑆
𝑑𝑈 = 𝑇𝑑𝑆 − 𝑃𝑑𝑉

5. To write the Maxwell relations we need
to concentrate on the direction of the
arrows and the natural variables only.
If both the arrows pointing in the same
direction, there is no need to change the
sign.
If both the arrows pointing in opposite
direction, there will be a negative sign.

6. A
Maxwell Relations

7. The four Maxwell Relations are important thermodynamic partial
derivatives which allow the substitution of measurable properties for
unmeasurable properties in thermodynamic relationships. Assuming
constant composition, they can be derived from the definition
equations of the basic reference properties.
These relationships can then be used to construct thermodynamic
diagrams. Examples for the most common diagrams are shown on
the next slide.

10.  The temperature versus the entropy diagram
 Lines of constant pressure curve from the lower left to
upper right on a T-S diagram.
 During an isentropic process there is no change in
the entropy of the system and the process is
reversible.
 An isentropic process appears as a vertical line on a
T-S diagram.
 The area under a process curve on a T-S diagram is
related to the amount of heat transferred to the gas.
T-S Diagram

11. It is possible to perform a series of processes, in which the
state is changed during each process, but the gas eventually
returns to its original state.
Such a series of processes is called a cycle and forms the
basis for understanding engines.
The Carnot Cycle describes the operation of refrigerators,
the Otto Cycle describes the operation of internal
combustion engines, and the Brayton Cycle describes the
operation of gas turbine engines. P-V and T-S diagrams are
often used to visualize the processes in a thermodynamic cycle
and help us better understand the thermodynamics of engines.

14.  The pressure-enthalpy (P-H) diagram is a useful tool
for refrigeration engineers and designers.
 It is also useful for service technicians.
 The P-H diagram is a graphical representation of the
refrigerant as it travels through the refrigeration
system.
 It can be used to predict several system conditions,
such as the pressure and temperature for the
refrigerant at various locations within the system.

17. In 1904, Mollier devised the first enthalpy-entropy chart still
most closely associated with his name.
Mollier's H-S diagram (Enthalpy v Entropy) was a logical
extension of the T-S diagram (Temperature v Entropy) first
proposed by Gibbs, retaining the advantages of T-S diagrams
but introducing several new advantages.
Mollier Diagram

20. Solve Example 6.7 by use of:
I. Mollier Diagram
II. Steam Tables

21. The important characteristic of the H-S diagram is that the ideal
adiabatic turbine can be conveniently plotted as a vertical line,
allowing a visual appreciation of the turbine performance.
We define the turbine adiabatic efficiency as follows:

22. The definition for the generic residual property is:
igR
MMM 
Where M is the molar value of any extensive thermodynamic
property, e.g., V, U, H, S, or G.
Note that M and Mig, the actual and ideal-gas properties, are at
the same temperature and pressure.
Residual Properties
The residual volume, for example, is:
P
RT
P
ZRT
P
RT
VVVV igR
  1Z
P
RT
VR

Other residual properties are defined in an analogous way.