THERMODYNAMICS
ANALYSIS ON CARNOT
AND
REVERSED CARNOT
HEAT ENGINE
Submitted by
Rahul Rauniyar - DTU/2K20/A2/03
Anand Karna - DTU/2K20/A2/21
Shashank Chaubey -
DTU/2K20/A2/22 Under the
supervision of
Prof. P.V. Ram
ACKNOWLEDGEMENT
Presentation, inspiration and motivation have
always played a key role in the success of any
venture.
We express our sincere thanks and pay our deep
sense of gratitude to Prof. P.V.Ram to encourage
us to the highest peak and to provide us the
opportunity to prepare the project. We are
immensely obliged to our friends for their elevating
inspiration, encouraging guidance and kind
supervision in the completion of our project.
We feel to acknowledge our indebtedness to our
sibling whose valuable guidance and kind
supervision given to us throughout the project,
shaped the work at its best show.
Last, but not the least, our parents are also an
important inspiration for us. So, with due regards,
we express our gratitude to them.
-Thank You
Rahul Rauniyar
Anand Karna
Shashank Chaubey
1.Abstract
CON TENTS
2.System Description
i. Carnot Engine
a. Tsource Versus Efficiency when Tsink is constant
b.Tsource Versus Work when Tsink is constant
c. Tsink Versus Efficiency when Tsource is constant
d.Tsink Versus Work when Tsource is constant
ii. Reversed Carnot Engine
a. Tsink Versus Work when Tsource is constant
b.Tsink Versus COP when Tsource is constant
3.Thermodynamic Analysis
i. Carnot Engine
ii. Reversed Carnot Engine
4.Result and Discussion
i. For Carnot Engine
ii. For Reversed Carnot Engine
5.Conclusion
6.References
ABSTRACT
The report deals with the thermodynamic analysis of Carnot and
reversed Carnot heat engines. A heat engine acts by transferring
energy from a warm region to a cool region of space and, in the
process, converting some of that energy to mechanical work is
Carnot Engine where the Reversed Carnot heat engine is a
device that transfers energy from an object at a lower temperature to
an object at a higher temperature by doing work on the system. As
the name, reverse heat engine the working principle of it is also
reverse of Carnot engine as it takes the heat from cold body and
supplies to hot body when external work is done on the system. The
analysis includes the calculations of work done and efficiency of a
Carnot engine with the help of temperature of source and sinks
including heat supplied to the Carnot engine while the calculation of
work done and coefficient of performance of reversed Carnot heat
engines with the help of temperatures of source and sink with
amount of heat absorbed from body at lower temperature. Then, the
graphs were plotted between temperature of sink and efficiency of a
Carnot engine keeping source temperature constant followed by the
graph between temperature of source and efficiency keeping sink
temperature constant. By the same way, another graphs
were plotted against the work done by the system keeping source
temperature constant for one graph followed by sink temperature
constant for next graph. These processes were also repeated for the
reversed Carnot engine but there will be the coefficient of
performance instead of efficiency. Hence, all these six graphs were
analyzed thermodynamically and the discussion was done on the
basis of those analysis. Finally, the conclusion was derived on the
basis of results and discussions.
SYSTEM DESCRIPTION
1. CARNOT HEAT ENGINE
Carnot engine is a theoretical thermodynamic cycle
proposed by Nicolas Leonard Sadi Carnot in 1824. Carnot
states that a hot body is required
that generates heat and a cold
body to which the caloric is
conveyed, which produces
mechanical work in the process.
It also states that said work is
free of the material that is used
to create heat and the construction and design material of
the machine.
Carnot Engine Principles
Carnot principles are just for cyclical devices such as
heat engines, which state that:
a) The effectiveness of an irreversible heat engine is
always less than the efficiency of a reversible one
functioning between the similar two reservoirs.
b) The effectiveness of all reversible heat engines
working between the
similar two reservoirs is
equal.
Carnot’s Theorem
It states, “No engine
working in a cyclic process
between two fixed temperatures of source and sink can
be more efficient than a reversible heat engine working
between some fixed temperatures of source and sink.” All
reversible heat engines working between the same fixed
temperature limits of source and sink will have the same
efficiency. 𝑄𝑠−𝑄𝑟
ηcarnot = = 1 - 𝑄𝑟 [ Tsink > Tsource]
𝑄𝑠 𝑄𝑠
Tsource−Tsink Tsink = 1 - T2
ηc = Tsource = 1- Tsource T1
2. RESERVED CARNOT HEAT ENGINE
The Carnot refrigeration cycle undergoes a process with the
opposite direction. The heat is absorbed from the low
temperature reservoir and then rejected to a high
temperature reservoir when some amount of work is
done. The Carnot cycle consists of two reversible
isothermal processes and two reversible adiabatic processes
which are reversed in the reversed heat engine. The
natural tendency of the heat is to flow from the high
temperature reservoir to the low temperature reservoir.
The reversed heat engine concept bolsters the findings
made by Clausius about second law of thermodynamics.
His statement for second law of thermodynamics says, “It
is impossible to construct a device which, operating in a
cycle, will produce no effect other than the transfer of
heat from a colder to a hotter body.” This means that
when the devise transfers heat from low temperature to
high temperature reservoir, it cannot do so
without producing any other effect. This any other effect is
absorbing the work. The heat will not flow
spontaneously form low temperature to high
temperature reservoir; some external
work has to be done on it.
Coefficient of Performance (COP)
a) For a Carnot refrigerator
COP
Heat absorbed from cold body Q1 Q1
R = = W = Q2−Q1
W
b)For a heat pump
COP
Heat delivered to hot body Q2 Q2
HP = = W =Q2−Q1
W
Thermodynamic Temperature Scale (Kelvin Scale)
For a heat engine, η HE
= 1 - Q2
[Q :1Heat supplied at T 1]
W
T2
For a reversible heat engine, ηRHE = 1 - T1
[Q2: Heat rejected at
T2] [T1>T2]
Applying Carnot Theorem, all RHE will have same η
while working in some fixed temperatures of source and
sink,
ηHE = ηRHE
Q1 = T1
or, Q2 T2
Thermodynamic Analysis
According to the given data, we have plotted some graphs
which give us vital information about how the processes in
Carnot heat engine and Reversed Carnot heat engine work.
Carnot Heat Engine
a. Tsource Versus Efficiency when Tsink is constant
When we keep the sink temperature and heat supplied
constant, and plot the graph between the temperature of the
source and efficiency, the obtained graph has positive slope
(straight line). On increasing the temperature, efficiency of
the system increases linearly.
b. Tsource Versus Work when Tsink is constant
Again, when we keep the sink temperature and heat
supplied constant, and plot the graph between the
temperature of the source and work, we again obtain a
straight line with positive slope. The decreasing slope
shows that the work done increases linearly on increasing
the temperature of the slope.
c. Tsink Versus Efficiency when Tsource is constant
When we keep the temperature of the source constant, and
plot the graph between temperature of the sink and work,
we observe that the work decreases when the temperature
of the sink increases.
d.Tsink Versus Work when Tsource is constant
When we plot the graph between the temperature of sink
and the efficiency, keeping the temperature of the source
constant, we see the efficiency decreases with increase in
the temperature of the sink.
Reversed Heat Engine
a)Tsink Versus Work when Tsource is constant
When we keep the source temperature constant and plot
the graph between the temperature of the sink and work,
we get a straight line with negative slope. This means,
the work decreases linearly with the increase in the
temperature of the sink.
b) Tsink Versus COP when Tsource is constant
Keeping the source temperature and heat supplied constant,
the graph is plotted for sink temperature against Coefficient
of performance and the graph obtained in curve is
increasing upward. This means that COP increases with the
increase in the sink temperature and decreases when sink
temperature decreases.
RESULT AND
DISCUSSION
FOR CARNOT HEAT ENGINE:
1. KEEPING SOURCE TEMPERATURE AND HEAT
SUPPLIED CONSTANT
Tsink VS Efficiency
The graph obtained is a straight line with decreasing slope
that shows that the efficiency decreases linearly on
increasing the sink temperature.
Tsink vs Work
The graph obtained is a straight line with decreasing slope
that shows that the work done decreases linearly on
increasing the sink temperature.
2. KEEPING SINK TEMPERATURE AND HEAT
SUPPLIED CONSTANT
Tsource vs Efficiency
The graph obtained is a straight line with positive slope that
shows that on increasing the temperature of source,
efficiency increases linearly.
Tsource vs Work
The graph obtained is a straight line with positive slope that
shows that on increasing the temperature of source, work
done increases linearly.
FOR REVERSE CARNOT ENGINE:
3. KEEPING SOURCE TEMPERATURE AND HEAT
SUPPLIED CONSTANT
Tsink vs Work
The graph obtained is a straight line with negative slop that
shows that on increasing the temperature of sink, work
done decreases linearly.
Tsink vs Coefficient of Performance
The graph obtained is Curve which is increasing upward
which shows that on increasing the sink temperature,
coefficient of performance increases and on decreasing the
sink temperature, COP decreases.
CONCLUSION
Efficiency of a Carnot’s engine depends only on
temperature of source and temperature of sink. It is
independent of nature of working substance and all other
factors.
Efficiency of cannot engine cannot be 100 percent
since sink temperature is never zero.
No irreversible engine can have efficiency more than
Carnot’s reversible engine working between same hot
and cold reservoirs. This is Carnot theorem
Coefficient of performance is always greater than one
for reversible Carnot engine.
REFERENCES
https://thermodynamics-engineer.com/429-2/
https://www.vedantu.com/physics/carnot-engine
https://www.brighthubengineering.com/thermodyna
mics/4531-what-is-thermodynamic-reversed-heat-engine
/
https://byjus.com/physics/carnot-engine/#:~:text=
Carnot%20engine%20is%20a%20theoretical,between%2
0two%20reservoirs%2C%20can%20possess.
https://en.wikipedia.org/wiki/Carnot_heat_engine
https://www.sciencedirect.com/topics/engineering/
carnot-engine
https://www.toppr.com/guides/physics/thermodyna
mics/carnot-engine/
