NATIONAL INSTITUTE OF TRANSPORT
FACULTY OF AVIATION TECHNOLOGY.
DEPARTMENT OF AERONAUTICAL ENGINEERING.
PROGRAM
: HDAME I
MODULE NAME
: ADVANCED ENGINEERING THEMODYAMICS
MODULE CODE
: AMU 07219
FACILITATOR’S NAME
: ENG.DR. SALUM CHANG'WARO
TASK
: INDIVIDUAL ASSIGNMENT 01
ACADEMIC YEAR
: 2024/2025
DATE OF SUBMISSION
: 11TH APRIL, 2025
NAME OF STUDENT
ENOCK CHRISPIN SHEKINYASHI
REGISTRATION NUMBER
NIT/BAME/2023/289
QUESTION:
With aid of diagram(s) describe in details the Path Function & Point Function.
A path function is a function whose value depends on the path taken to reach a particular state. It is not
a property of the system but rather a boundary phenomenon,
Figure 1: Graph of P-V showing Example of the path function
In the P-V diagram has the same initial and final states of the system, but work done in all the three
processes is different. For process A work done is b2A1a, for process B work done is b2B1a, For process
C work done is b2C1a
a). Examples of Path Functions
i. Work (W) as a Path Function; Work done on a system depends on how pressure and volume change
during the process. The work done in expansion or compression can vary if the path is isothermal,
adiabatic, or polytropic. If a gas expands slowly or rapidly, the work done will be different, even if the
final and initial states are identical.
ii. Heat Transfer (Q) as a Path Function; Heat depends on the method used to transfer energy—whether
heating is constant, rapid, or involves phase changes.
b). Characteristics of Path Functions
i. Process-Dependent; Their values change based on how the transition occurs, not just the initial and
final states.
ii. Different Paths Lead to Different Values; Even if a system reaches the same final state, varying paths
can result in different amounts of work or heat transfer.
iii. Inexact Differentials; Represented using δ instead of d in equations, showing they are not state
properties.
A point function (also called a state function) is a quantity that depends only on the initial and final states
of the system, regardless of the path taken. Examples include internal energy, entropy, enthalpy, and
temperature.
Figure 2: graph of P-V showing example of point function
a). Examples of Point Function
i. Internal Energy (U) as a Point Function; If a gas in a container undergoes expansion or compression,
its internal energy depends only on its initial and final states, regardless of whether heat or work was
applied rapidly or slowly.
ii. Temperature (T) as a Point Function; If water is heated from 20°C to 80°C, the temperature change
remains 60°C, no matter how fast or slow the heating process occurs.
iii. Enthalpy (H) as a Point Function; If steam is generated from water, the enthalpy change is fixed for
the given initial and final states.
b). Characteristics of Point Functions
i. State-Dependent; Point functions rely only on the initial and final states of a system.
ii. Exact Differentials; meaning they can be integrated directly.
Relationship Between Work and Internal Energy
In thermodynamics, point functions and path functions are closely related because point functions
describe the system's state, while path functions determine how the system reaches that state. Path
functions like heat (Q) and work (W) affect point functions such as internal energy (U), enthalpy (H),
and entropy (S). The process of energy transfer (path function) changes the state properties of the system
(point function). Such relations are
i. Path functions (heat and work) drive changes in point functions (state properties).
ii. Different paths result in different values of heat and work but still yield the same final point function
values.
iii. Point functions establish boundaries or limits for how path functions behave in thermodynamic
systems.
Difference between point function and path function
i. Point function Its values are independent of the path followed, but path function Its values are
dependent on the path followed
ii. Point function Its values are based on the state of the system like pressure, volume, temperature. But
path function Its values are based on how that particular thermodynamic state is achieved.
iii. Point function, no matter by which process the state is obtained, its values will always remain the
same. But path function Different processes to obtain a particular state will give us different values.
Iv. In point function Only initial and final states of the process are sufficient. while in Path function We
need to know exact path followed by the process
v. Point function It is an exact or perfect differential, while path function It is an inexact or imperfect
differential.
vi. Since a point function is only dependent on the initial or final state of the system, hence in a cyclic
process value of a thermodynamic function is zero. But for path function Its cyclic integral or process
may not be zero
Figure 3. Difference between Point function and Path function
REFERENCES
(n.d.).
cengel, Y. A. (26 June 2019). Thermodynamics: An Engineering Approach | 9th Edition. India :
McGraw Hill.
Zemansky, M. W. (2020). Heat & Thermodynamics. Delh, india: McGraw Hill Education.