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On this topic, we (wikitec Team) have tried to explore the complete analysis of the thermal engineering portion or, you may say, thermodynamics with all of its applied formulas and its basic concepts in competitive or semester-wise examinations. Dear aspirant, please take a moment to read the full articles, which will be your appreciation and trust in us as we help you achieve your goals.
Table of Contents:
The First law of
Thermodynamics:
Closed System
Analysis:
Energy Balance:
Energy of an
Isolated System:
Enthalpy:
Change in Energy
of a System:
Perpetual Motion
Machines:
The Second law
of Thermodynamics:
Thermal Energy
Reservoir:
Heat Engine:
Refrigerator:
Perpetual Motion
Machine Kind of Three:
Conclusion:
The First law of Thermodynamics:Closed System Analysis:Energy Balance:Energy of an
Isolated System:
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Here, we have discussed about different laws and its forms of energy in Thermodynamics. And also, we have considered some symbolic representation of heat as Q, work as W and total energy as E respectively during a process.
So, let’s begin with the analysis of First law .
The First law of Thermodynamics:
Basically, the first law of Thermodynamics deals with the
various forms of energy interaction. This law implies that the principle of
energy conservation, that’s mean Energy never be created nor destroyed, only option
is left for changing into various forms.
Let’s take an example, when a stone at some height having its
in-built storage of potential energy, until it falls down. But once it falls
down due to gravity of the earth, a stone acquires kinetic energy, which will convert from potential
energy during the process.
As per the experimental observations, if we decrease the
potential energy of an object, then we must see that the kinetic energy
ultimately increases.
You may see the below figure for your better understanding
here.
Here, from the above figure, we have found that the decrease
in potential energy [(mg∆h) = m(Square of V2 - Square of V1)/2] is the increase in kinetic energy.
Where, m=mass of a stone
g= acceleration due to gravity
∆h=change in height
V2=Final velocity &V1=Initial Velocity
Now, we have taken another process of a system. For the adiabatic (non-interaction of heat transfer) condition, here we see for the consideration two states under P-V diagram of a Closed System, the net work done is equal to the type of the closed system as well as its process.
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| Cycle under Adiabatic Process |
From the above P-V diagram, we have found that ∑Q=J(∑W)
Where J= Joule’s equivalent
∮ dW1-2 = ∮ dQ2-1
∮
can be expressed
as cyclic integral of closed path of a system.
In
SI system of units for both work and heat transfer can be considered as Joule(J=1Nm/J).
So,
the First law of Thermodynamics can also be expressed as the property of total
energy E is same to the net work done under adiabatic process of a closed
system between two states. The net value of work should be valid at the final state of a system.
Hence, the change of net energy in adiabatic process should be equal to the net work done during a process.
Here, there are so many examples, you may
consider like the increase of energy of a potato in an oven, which is equal to
the amount heat transferred to it.
Similarly,
if we take another example of heating of water in a pan at the top position, then
the heat transfer occurs from heating element (pan) to the water.
Next,
we can take an example of well insulated room (adiabatic condition), which is
heated by an electric room heater. Here, the heating energy will be increased
until system undergoes adiabatic condition. That’s mean, there is not heat
transfer occurring to or from the surrounding. In such situation, you may take Q=0.
Here,
there is another interesting point to be remembered Caloric Theory of Heat.
The
caloric theory of heat is generally considered as an invisible fluid flow from
higher body temperature to lower body temperature.
Here,
if we consider paddle wheel enclosed in the fluid under adiabatic condition
with some weights with a pulley arrangement system, then we will see one thing
that the net work done on the system must record as an increase in energy of a
system without interaction heat between system and its surroundings.
First Law of Thermodynamics for
Closed System Analysis:
For the cyclic process of Closed System, there is an
expression like sum of all energy transfer across the boundaries should be zero
as ∑Q=∑W.
Here, we take a system, which undergoes the change of state during
both heat and work transfer, the net storage of heat energy transfer is to be
considered within the system.
.png) |
| Heat(Q) & Work(W) of System |
Let suppose Q is the net heat transfer to the system, where
W is the net work transfer from the system in a process.
Now, we consider Q-W is the amount of net energy
transfer to the system, which will be stored in the system.
N.B: - So, here point to be noted that Energy in storage form never be assumed
as heat or work, it’s only considered as the internal energy of a system.
Now, we have an expression on this above short discussion
that
Q-W=∇E
Or we can write this
such like Q=∇E+
W
Where, ∇E is
considered as change in energy in a system.
Some Important Points:
- For an Isolated System, the energy(E) will be constant throughout the process.
- Energy is an extensive property, but specific energy is an intensive property, which has discussed earlier.
- Energy is Point function and also a property of a system.
- For an Ideal gas, the internal energy (U) depends on temperature.
Energy Balance:
Here, we have considered that the net change in total energy (which
may increase or decrease) of the system is equal to the difference between the total
energy incoming and total energy extracting in the system during the process.
That’s mean (Ein-Eout= ∇Esystem)
Ein=Total energy entering
Eout=
Total energy leaving
∇Esystem =Total energy change
Energy of an Isolated System:
Here, we
have known about an Isolated System that there is no interaction of heat with
respect to surroundings.
For an
isolated system; dQ=0, dW=0
As per the first
law of thermodynamics, dE=0;
That’s mean for an isolated system, the energy of is always constant; E=Constant
Enthalpy:
If
we analyse about the enthalpy, then we always see that there are the two combined
properties of u+Pv.
For
our better understanding, you may say it a new property h=u+Pv kJ/kg
or
H=U+PV kJ
The
above both expressions can be referred to as enthalpy. But here h is
simply referred to as specific enthalpy, where
H is referred to as total enthalpy.
Here
the both above equations are homogeneous dimensionally.
The
combination of u+Pv,
which is frequently considered as the
analysis of control volume, especially for the power generation refrigeration
system analysis.
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| Control Volume Analysis under u+Pv |
Change in Energy of a System (∇Esystem):
Here, we have discussed about the energy change of a system during
the process involvement for the energy of a system from the beginning state to
ending state. That’s mean their difference between the energy change of a
system is
∇Esystem=Efinal – Einitial
As, we have known that energy is property of a system and its
value does not change until both the final and initial states change. The
energy is considered to be zero, when the state of a system is constant during
process. Where the energy can exist in various forms of internal energy, kinetic
energy, potential energy, electric energy etc.
If we consider total summation of these energies, then we get the total energy E of a system.
∇E= ∇U+∇KE+∇PE
N.B:
- The above expression will be valid
only for simple compressible system with the absence of electric, magnetic and
surface tension.
Now we have
discussed another part of thermodynamics laws behind some principles.
Perpetual Motion Machines:
Here, we have two kinds of machine. Such as perpetual motion
machine first kind (PMM1) and as perpetual motion machine second kind (PMM2). Often,
both the two kinds of machine PMM1 & PMM2 are hypothetical kind. It is
impossible to obey the both rules like first law and second law of
thermodynamics. We he discussed about briefly here.
Firstly, we have discussed about the Perpetual Motion Machine
First kind (PMM1). Here as per the PMM1 kind of machine, it says that
producing the continuous mechanical work without supply of energy or you may
say any kind of external agent. But its violets the principle or the first law
of thermodynamics. Such kind of fictitious machine is called as Perpetual
Motion Machine First kind (PMM1).
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| Perpetual
Motion Machine first kind (PMM1) |
Secondly, about the Perpetual Motion Machine Second kind (PMM2), it always demands that 100% efficient kind of machine, but unfortunately its violets the second law of thermodynamics. How it possible, let’s see. As per the PMM2 kind of machine, some of the heat is transferring to the system boundary and then exhausting to the environment through condenser, but here point is that the exhausted heat in the form of steam to turbine to pump for producing work, thus System boundary will have a 100% theoretical efficiency. Such kind of fictitious machine called as perpetual motion machine second kind (PMM2). Such kind of conception was totally wrong. It’s also violating Kelvin-Planck rule.
The Second Law of Thermodynamics:
Basically, the
second law of thermodynamics is used to evaluate the theoretical limits for the
performance of all engineering systems and devices such like thermal
reservoirs, heat engines, heat pumps and refrigerators etc. And also
considering the degree of completion of reactions.
Here, we have introduced both high grade and low-grade energy.
If we consider high grade energy as Work and low-grade energy as Heat, then the
conversion of low-grade energy into high grade energy during a cycle, which is
absolutely impossible. How it possible: it’s not possible at all. Yes! possible
if we convert high grade into low grade.
N.B.: - For this, we can consider Work as high-grade energy
and Heat as low-grade energy always.
The point to be noted as per the Joule’s principle that
if we supply the energy to a system in the form of work then we will see work
can convert into heat as well, but heat cannot convert into work during a cycle,
which is absolutely not possible.
N.B.: - So, the work & heat are not interchangeable
Here, we have discussed some conditions.
If we convert work (W) into heat (Q), then we can write W=Q (→)
Similarly, if we convert heat (Q) into work (W), then we have
Q>W (→)
Here, the arrow (→) has indicated the energy transformation
in a direction.
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| Second Law of Thermodynamics |
The efficiency of heat engine is always η= Wnet/Q
N.B. :- Always the efficiency should less than unity.
So, as per the Kelvin-Planck rule's second law of Thermodynamics, a heat engine can not produce 100% efficiency; Q>0.
Form the above figure, we have already known that the
efficiency of a heat engine is η= Wnet/Q =1-Q1/Q2
If we consider Q2 = 0, then Wnet= Q1
Or we may say η=1
That’s mean, if a heat engine will produce net work done
during a cycle by exchanging heat by the help of single reservoir, thus it
completely violets the Kelvin-Planck rule's second law of Thermodynamics.
N.B. :- To be noted that never intersect exist between two reversible adiabatic paths, which will violet Kelvin-Planck rule's second law of Thermodynamics
Similarly, we consider another statement of Clausius’s Second
law of Thermodynamics.
In this case, we have already discussed higher temperature
grade and lower temperature grade. As per this law of statement, we conclude
that it is impossible to develop an engine during a cycle, which will produce
no effect other than the heat will transfer from lower temperature to higher
temperature grade.
Now, we have
discussed about the Thermal Reservoir.
Thermal Energy Reservoir:
With
reference to Second law of thermodynamics, it is very easy to understand about
a hypothetical engine having large thermal energy capacity, which we can apply
or absorb the quantity of heat without change in temperature.
Here, we
consider as a reservoir which supply energy in the form of heat is known as Source.
And the reservoir
which absorb energy in the form of heat is known as Sink.
Next. We can
discuss about Heat Engine.
Heat Engine:
The term
heat engine is basically used as work producing devices. Heat engine is
considered as thermodynamic cycle, where the net heat (Qnet) transfer to a system and total work (Wnet) transfer from a system.
Here, we
should know that work can be converted into heat but heat into work for such
case, we require some external devices, which are known as Heat engines.
We may say
by taking some considerations that the heat transfer occurs from higher
temperature source like solar energy, oil furnace and nuclear reactor.
The conversion
of heat into work usually occurs by rotating shaft and exhaust some heat to the
lower temperature (sink) like pond, rivers and atmosphere during a cycle.
Now let’s take
an example
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Heat Engine Source and Sink at T1 & T2 |
ηth=
Wnet/Q1 =Qnet/Q=1-Q2/Q1
Or we may write this as ηth for reversible= 1-T2/T1
Where, ηth=Thermal efficiency
Wnet=Net work done by steam
Q1=Heat Supply from source at T1
Q2=Heat rejects from sink at T2
Heat Pump:
Basically, the heat transfer occurs in such case from lower
temperature source (sink) to higher temperature source(source).
 |
Heat Pump at source T1 and sink T2 |
(C.O.P.)HP= Output/Input=Qout/Winput
Winput= Q1- Q2
Also, we have another expression from above state
(C.O.P.)HP= Q1/ Q1- Q2
For reversible
cycle, (C.O.P.)HP= T1/ T1-T2
Where, C.O.P. means Co-efficient of performance
Refrigerator:
The main objective of a refrigerator is that the extraction
of heat from lower temperature body to higher temperature body.
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| Refrigerator at source T1 and T2 |
Here, there is a relation between Heat pump and Refrigerator
(C.O.P)HP=(C.O.P)refrigerator+1
N.B.
:- These above all expressions are applicable for both reversible and irreversible
cycles.
Here, we have some considerations, you have to note it down
Let suppose two reversible engines operating between different temperature limits
at T1, T2, T3.
Where T1>T2>T3,
Now we may see this below figure under
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Two reversible engines work thermal reservoir at T1 T2 T3 |
For the case study for both engines are as followed; point to be noted W1 & W2 by the system.
Case-1 If we consider for both engines have same efficiency, then
T2= √(T1T3)
Case-2 If we consider for both engines have same work input, then
T2= T1+T3/2
Perpetual Motion Machine of Kind Three:
We have already discussed two kinds of machine
PMM1 and PMM2 earlier, but now we will discuss about Perpetual Motion Machine
of third kind (PMM3).
The perpetual motion machine of the third kind
deals with friction mechanism. Friction is always involved in all movable
devices. Without Friction, we cannot control over motion in our daily life. We
cannot eliminate the friction factor completely. If it would have possible, all
movable device in continuous motion without violating the thermodynamics laws.
Hence, the continual motion of a movable
device without friction is called as Perpetual Motion Machine of third kind (PMM3).The
friction may be irreversible that should be executed by second law of
thermodynamics.
Conclusion:
In
this post-discussion, we are emphasizing the point-to-point bullet lines, or,
concisely, the topic of laws of thermodynamics, or you may say first and second
law of thermodynamics, only with most relevant and important explanations, as
well as its formulas to help our readers with their revision and enable them to
move confidently towards success. We wish you to ace your path significantly.
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