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Good afternoon. I welcome you all to this session of basic thermodynamics. The last
class, we discussed the concept of energy from thermodynamic view point. Energy is in
two forms: one is energy in transit, that is, work and heat transfer which are part
functions; and, another form of energy is energy in storage, that means, stored in a
system; they are point functions and they describe the property of a system.
Today, before starting the first law, we will discuss the different forms of work transfer.
In this connection, I tell you that we have already appreciated that all energy transfer,
that means, energy in transit is categorized in two forms: one is heat transfer that is
why hot spot temperature difference; another is work transfer, so, electrical work, mechanical
work, magnetic work and all are there. Conventionally, when you call work transfer without any other
adjective, heat into mechanical work transfer. Otherwise, we tell electrical work transfer,
magnetic work transfer and all these things Now, we will recognize some important forms
of work transfer, mechanical work transfer, first. Then, we will switch over to the first
law of thermodynamics.
Different types of work transfer: This is like this, displacement or pdV work, I will
explain each and every one, paddle wheel work, you can write this, flow work and shaft work.
These are the different types of work transfer: displacement or pdV work, paddle wheel work,
flow work and shaft work. These are all mechanical work transfer between the system and its surrounding.
The only work transfer is mechanical work transfer between the system and the surrounding.
Now out of these, the most important and difficult to understand at certain stage is the displacement
or pdV work, the first one.
Let us see, what is the displacement or pdV work. Displacement or pdV work is associated
with a closed system. Let us consider a closed system, specified by some properties; let
X, Y be the two independent properties, two fixed state. This displacement work is because
of the displacement of the system bounded that means, this is the closed system; there
is no restriction whether its volume will be fixed; the system boundary can either expand
or collapse. Because of the displacement of the system boundary, containing a fixed mass
of fixed identity, the work transfer which takes place with the surrounding is the displacement
work. But there is a specific theme in between what is that? The displacement work specifically
implies the work because of the displacement of the system boundary in a quasi equilibrium
process, why that work pdV comes will be understood after, that means, system has to expand or
collapsed slowly through limited equilibrium states. If you consider a system like this
where pressure is exerted on the boundary. Let the system is at equilibrium state and
a pressure p is exerted at the system boundary Now, we consider it equilibrium when the system
boundary is at that it cannot be standard stress if there is a difference in pressure
it will expand or collapse. So, it will be equilibrium when the external pressure imposed
on this boundary. Let me denote it pex, external pressure equals to the pressure inside the
system which is uniform throughout the system and external pressure is also uniform throughout
the system; under this situation only, the system will be in equilibrium
If we consider the system expands for example, the boundary expands, in such a way that all
the time there is an infinite small pressure imbalance, that means, In the theoretical
sense, we consider at the system expands when both the internal pressure and the external
pressure that is, internal force due to this pressure and the external force due to this
external pressure always balance each other. Under this condition, the system boundary
expands or collapses. Then this work is known as displacement work. By doing so the system
attains another state for example, state one to state two. The state one is characterized
by pressure p1v1 and state two is characterized by pressure p2v2. It attains the state like
this where the volume is increased and the pressure is decreased. Through such quasi
equilibrium state, that means, it expands slowly when infinite small amount always in
a theoretical sense with a balance between the internal and external pressure.
In a limiting case, in practice to conceive it, we consider the imbalance as infinite
small, so that it finally attains this stage. Then the work which is finally transferred
to the surrounding, in this case, when it expands the work will come out of the system
which is given by integral of p into dV. We cannot evaluate this integral until or unless
we know p has a function of v. That will be found out from some concerning law of the
process, but this work done can be written as integral pdV from state one to two, so
this equals to the work done. That is why this displacement work is told or named as
pdV work.
But to understand this, I think it will be better if we follow this one which we discussed
last class, in relation to quasi equilibrium process. Let us consider this, how to understand
this? Because here if I describe these, this thing works as information, understanding
is less. Let us understand how this work becomes pdV
work. Let us consider quasi equilibrium expansion of a gas in a cylinder; this is the resting
piston. Now, this is a stage when this piston carries somewhere w which is divided into
number of infinite small amount of works that means, infinite large number of works divided
like this. Now, this gas has a pressure p and volume v. Let us consider this as the
initial stage. This gas is within the cylinder and piston represents a closed system bounded
by the system boundary. One of the boundary pistons is movable so that displacement work
comes into picture, that is, the system boundary is displaced
As I explained in the last class, what we can do is let us think that there are stops
like that, that if we gradually release the way so the gas expands slowly in a gradual
manner. First, let us go through like this. Initially, at the first moment, the weight
and the external pressure if any, they balance the internal pressure force. That means, this
weight plus the force due to any external pressure, if there is any external pressure,
is p external. They balance the force caused by the internal pressure on the cylinder.
So this is in equilibrium position, the simple mechanics. If we release a small weight so
that an infinite small imbalance is created; then, the piston moves by an amount delta
z which is very small In this case what we do? If we make the small
movement and slow movement of the piston, the dissipative effect is absent; friction
is all most absent. In the ideal case, we can consider the piston to be frictionless,
but even if there is friction in a slow motion, the friction is almost absent. So, what happens?
This moves by a distance delta z. What is the work done in this case? The work done
is that now this weight w, let us consider the weight w is the net force that includes
both the forces weight: this weight and the forces due to external pressure; this weight
balance the p into the area When this is moved to a distance delta z,
this means that this force has a displacement delta z as if this total weight w, which is
been balanced by the pressure force this side of the piston is being lifted against gravity
by an amount delta z. So, that is the work done? Work done is p A deltaz that means p
into dV, dV is the volume; it is the short of non-dissipative work, the change in the
potential energy of the weight is w into delta z, that is, w is delta z p into A. This is
w, work transfer is also w. The nomenclature is confusing, so let us consider this as small
w otherwise there will be confusing. This is the small w weight; so, small w is p into
A. So, work transfer w will be p into A delta z, which will be equal to the small weight
If we do so in infinite small interval and number of infinite number of paths so that
ultimately it comes to this stage where we attained as state two for example this is
state one this is state two from state one to state two then we can write that w from
state 1 to 2 is the integral of pdV from 1 to 2. This is the work done, that is, the
pdV work. Always, we consider a small distance slowly.
If you cause a large displacement of the piston then force into displacement; that work is
a dissipative work in nature. This is a non-dissipative work like the work done in a conservative
force paid. Always the work which is been done to leave this weight to a small incremental
distance delta z that means, all these works are at non-dissipative work. When you consider
some weight this is coming from this position to this position, the difference in potential
energy is actually the work delivered by the piston because no work is being dissipated.
This is the way one can conceive that if there is a closed system which has a pressure p
and volume v initially, for example p1 and v1 and come to a state p2 and v2 by expansion
through a series of quasi equilibrium states. Then the non-dissipative work which comes
out is equal to integral p dV and this work is known as displacement work or pdV work
and sometimes this is known as reversible work. We will discuss the word reversible
while i teach you the second law of thermodynamics because this process is the reversible process.
If you want to go back from this position again to the initial position through same
quasi equilibrium states you will get back this work which you will not be doing so.
Because if there is a mass of gas, there is a piston, if you just expand first not through quasi
equilibrium state and natural expansion of gas from one state one to state two, if you
measure the work done by any work measuring instrument and if you compress the piston
again from state two to state one and if you measure the work required to return its step
one, similar to the initial state from state two, you will see the two works are not required.
This is because the dissipative work which has been lost in friction is not the same
for both forward and reverse processes Because of these stresses, I will explain
the process is not reversible. Though the system comes back through initial state there
is a change from the surrounding because surrounding got some work earlier and surrounding has
given some different work afterwards to return the system to its initial state. Keep it in
mind when I discuss the reversible process, I will come to the same point. If you consider
a non stresses work through quasi equilibrium states this work equals to integral pdV when
the displacement of the system boundary of a closed system takes place. So, we come to
the next one. This is very simple, paddle wheel work.
Paddle wheel work is very simple as the name itself tells what a paddle wheel work is.
If we consider some liquid or some fluid, better to consider liquid, some liquid in
a container and if you stir it with a stirrer or paddle wheel, rotate it. What is this?
By physics, very simple, you stir a paddle wheel or a stirrer in a liquid, its temperature
is less. What is done basically? Work is been transferred to this system that means we take
this as a system then we can tell what transfer takes place across the system boundary. Work
has come from the surrounding to the system which has caused this property to change.
It may be denoted by initial property x1, y1, any two thermodynamic property, the properties
are change to x2, y2. In fact we know what happens; the temperature
is increased. Today we can tell that because of the work transfer the internal energy increases,
but this type of work transfer is known as paddle work or stirring work. One of the very
important difference between the pdV work and this work is here friction is very important.
Because of the friction the work is done. Because if you want to rotate the stirrer
or paddle wheel within a fluid as a system. If the fluid has no friction no viscosity,
so no work is required to rotate it. Here friction is the agent for the work to be transferred
to the system. This is the dissipative work but it is a work transfer. If you think from
the thermodynamic point of view, if you define these are the system and if i ask what is
the energy transfer, you tell work transfer because of the rotation of the paddle wheel.
This work transfer cause a change in the state of the system from any two independent thermodynamic
properties to other two independent thermodynamic properties to define the different states
In fact, what happens is that the temperature is changed and if the temperature is changed
some other properties will be changing according to the relationship of the different properties.
So this is a kind of work transfer which is the irreversible work transfer which means
this is dissipative in nature and here friction is the agent for transferring the work. This
is known as paddle wheel work or stirrer work, sometimes stirring work. These stirring energies
are important. When you solve problems you will see some paddle wheel work among this,
so this is paddle wheel work Another is the flow work. Flow work, probably,
you have already heard or you have already read in fluid mechanics. What is flow work?
Flow work is the work required to maintain a flow. What happens when there is a continuous
flow? You see paddle wheel work and the pdV work part into closed system. Now, the flow
work part into a control volume and there is a steady flow of fluid, a steady flow of
masses and steady flow of matter; coming into the system, going out of the system, control
volume system or control volume When a steady flow occurs or it may be unsteady
flow, any flow occurs at any section to maintain the flow, if you consider a layer at any section
it has to continuously move. That means if you make a Lagrangean approach, for example,
of fluid mechanics we tell layer, you see the layer has to always push the neighboring
layer to make it go through just like you going in a queue that when you are in a queue
you have to always push your neighboring person in front of you to make your way through.
Therefore, each and every section does some work in the neighboring fluid, that means,
the adjacent section, downstream to make it so a through. So by this it does work on its
adjacent neighboring downstream layer. This work is known as flow work and because of
this work, again, the adjacent neighboring layer which receives this work stores some
form of energy. We can tell always that at any section there is some stored energy in
the fluid by virtue of which it can do work on its neighboring layer to make it so a through.
This is the basic concept. This work is known as flow work and the energy by which it can
do so is known as pressured energy. So, pressured energy and flow work are the two synonymous
things. In case of fluid mechanics, we call it is as pressured energy, this is the convention.
In case of thermodynamics, dealing with this thing, we tell it as flow work. Let us again
recapitulate this flow work and you know probably from fluid mechanics, the expression of the
flow work in a flowing system, if you denote the pressure at a section p and density of
the fluid is rho then flow work or pressured energy is p by rho or p into small v, where
small v is the specific volume one by rho. Let us recapitulate this again.
This is the basic definition. Now, let us consider a control volume. We know what a
control volume is. There is a continuous mass coming in. Let us consider this is the inlet
and let us consider this is the outlet. This is a typical practical control volume. The
practical examples are like a control volume may be an air compressor as you know what
the function of air compression is. It receives air at low pressure and temperature continuously;
then, compress it because of some thermo machinery action within it that I am not going to discuss
here because that is beyond the subject of basic thermodynamic, we consider this as a
black box. Finally, it delivers the work, air at high
pressure and temperature. It can be a turbine where high pressure and high temperature gas
or air is received and it is been delivered at a lower pressure and temperature. In doing
so, the control volume either develops work in case of turbine or receives work in case
of compression. There are other examples, heat exchangers
where there is a continuous in flow of material and continuous out flow of material. So they
are the examples of control volume systems turbines, compressors and heat exchanger.
Let us consider such a control volume and we too understand the flow work. Let us consider
some amount of mass here at the adjacent boundary of the control volume; this is dx; let this
mass amount be dm. Let us consider this amount of mass has to be forced into the control
volume by against the pressure that means this has to be done. For example, here a pressure
existing against at this boundary of the control volume let it be p. The situation is like
that to understand it again, that against a pressure p here, we have to force this amount
of mass into the control volume whose amount is dm. How to do it? To conceive it, for understanding,
you can think this way that for example, this is the fluid; the fluid in this left side
that means, upstream side of this identified mass acts as the piston to force it through
the control volume. If we do that you can draw the diagram again. We can consider this
mass like dx and here we can conceive the fluid acting as a piston, just for our understanding,
hypothetical piston which is pushing. This is nothing but the fluid behind this upstream
pushing this, through this. So, what is the work done? The force on this piston will be
against this pressure p which is prevailing here also, the small elemental mass; let the
cross sectional area is A, so p into A. The work done is p into A into dx. This work,
while it is done on this layer, on this element of fluid, not layer, we have identified a
small amount of mass. This is stored in the mass as energy which is pressure energy; this
causes the control volume. This is usually expressed per unit mass; this is the convention
work done on this mass per unit mass or the energy stored in this elemental mass per unit;
mass will be p A dx divided by, what is the mass, rho into A dx A, where dx is the volume,
rho is the density. This comes out to be p by rho in thermodynamics. We do not deal with
rho; we usually deal with specific volume, one by rho.
Therefore, this p v is the flow work. The definition of flow work is the work that is
required to push certain amount of fluid across a section in a flow process or in a control
volume. If in a limiting case and dx tends to zero, we can define the flow work per unit
mass at each and every section because these are the point functions. This is the expression
of flow work. Next is the shaft work. What is a shaft work?
Shaft work is again pertaining to a control volume or a steady flow process that we will
appreciate afterwards.
Sometimes what happens when there is a control volume, again we will see because of continuous in flow of matter, as i have told, in case of air compressor
or turbine some work is delivered by the control volume or some work is taken by the control
volume in case of work interacting devices like air compression and turbine and this
work has been obtained or has been given through a rotating shaft against a resistance torque
and that is known as shaft work. We make a diagram like that. There is a shaft rotating
turbine; it develops power or work to the surrounding through the rotation of a shaft
against a resistance torque. Similar case for air compressor or any compressor or a
pump, when the work is being given to the control volume, this is, giving through the
rotation of a shaft against a resistance torque. This work is named or categorized as shaft
work. These are the different forms of mechanical work transfer.
At the end of this discussion, I like to mention very emphatically this thing we now know that
work and heat are very important path functions. What does it mean? These are the work energy
in transit; let us think that a thermodynamic coordinate diagram y x and if a process starts
from state one and goes to state two with property X1, Y1 and any two independent intensity
property X2, Y2. If there is a work and heat interactions let us consider work is coming
out in this process w and heat is being given Q in a different direction i assume, then
the thing is that this work for this path is fixed but it depends upon these two paths.
We can write this W as W1 if we specify the path as some middle quantity A1 A2 which is
not equal to W1- W2; though this is very simple today, but still you should be aware in mind.
Similarly, Q1-A-2 is the heat which is been given to the system in this process but which
is not equal to Q1-Q-2 which means that if we have an another path for example we make
the system to go through another path from state one to state two through a path 1B2,
in that case W1-B-2 will not be equal to W1-A-2 because they are path function. If the work
develops is W1-B-2 then this is not same; if the heat given in this path is Q1-B-2.
So, Q1-B-2 is not equal to Q1-A-2 means that even if the system connects to terminal state
points same to terminal state point, but through different path, work and heat interactions
through different paths are not same because they are not path functions. But if anybody
asks what is the change in its property in this path 1A2 you tell the change in property
is X2-X1, property X; property Y is Y2-Y1 if anybody ask what is the change in property
X and Y when a system performs a path 1B2 from the same state point A to the same state
point B, then the change will be same because they are point functions their values are
associated with this state point. so whichever may be the path, their changes
will remain the same; whereas, work and heat are not path functions; they depend only on
the path so the work interactions in different paths will be differ and they depend only
on the path. They are not described to the state of the system, this is very important
while the internal energy or energy stored within the system, that is, the point function
which is stored at the state points. I will come afterwards while discussing the first
law of thermodynamics. Now I come to the first law of thermodynamics.
Let us ask what is first law of thermodynamics? First law of thermodynamics is nothing different
from the conservation of energy; it is a look from a different angle. So, first law of thermodynamics,
first line of definition, if anybody asks, what is the first law of thermodynamics? It
is conservation of energy. The first law of thermodynamics is stated
in the thermodynamic field of thermodynamics in a different way. When we are concerned
about the conversion from heat to work or work to heat this is basically the way the
first law of thermodynamics originated. However, first law of thermodynamics in a broad sense
is the conservation of energy, but this will be defined the same conservation of energy
principle in terms of the processes which converts heat to work or work to heat. We
will be concentrating the discussion on first law in relation to conversion of heat to work
and work to heat. Before giving you a formal statement of the
conservation of energy, in this regard, as the first law of thermodynamics, let us see
that how it was first discovered or originated by the great scientist Joule.
Let us go through Joules experiment which is again a recapitulation of what you have
read at school level, what Joule did.
Let us consider the Joules experiment. First take two k container where there is water
for example, let water and the well. Let a paddle wheel or a stirrer be rotated and the
entire system is insulated; no heat is being allowed; let this be also closed and insulated.
Let a thermometer be dipped into it, the way Joule did the experiment. He rotated the stirrer
for some time and then stopped. What happened, tell me? Some amount of work cross the system
boundary that means it has come from the surrounding to the system for which the temperature has
raised; the system state has changed. Then Joule observed that because of this work transfer
into the system there is a change of state which is manifested by the raising temperature;
did he also measure the pressure? He found the pressure remains all most the same. What
he did after that? He took this same container well, same container with the water and made
it insulated for example by the sides. Let it be closed and in one side of it, it made
a contact with a hot body We simply mean that the added heat to the
system and he found that the same temperature rise can be observed by giving a calculated
amount of heat and the same change of the state. What concluded into thing that moment
probably today you will laugh at him because this was some hundred fifty years back that
people use to think before that the heat and work are the two things at entirely different
quantity. They may be the energy transfer but they do
not have any link with each other. It was Joule first to point it out from this simple
experiment that work and heat can produce the same effect on a system and they two cannot
be different type of energy transfer though may be different afterwards the difference
will be proved in second law but they are all most same type of energy transfer by producing
the effect in a system. Both these things can produce the same effect in a system.
Then little farther what he did there. Now come back to this diagram that means some
work transfer took place and the system temperature increase. Now, we remove this insulation,
what it did? When we recognize this one that giving heat temperature can be increased what
he did, we took a bigger bath water containing cold water that means this is cold water.
What happen heat comes out from the system to this cold water and he restored the initial
state by reading the thermometer that means the initial state of the water from where
the stirrer where the transfer the work to resist temperature, then he found the amount
of heat which was coming out because of this which is the exactly the same which was giving
to resist temperature and at the same time this becomes exactly equal to the work and
he took different fluid and a different container different time and he always found is heat
and work is same by doing this experiment. Now, if I draw this in a cycle here, how can
I show it in a thermodynamic cycle Y,X. For example, the first one is a process it goes
from state 1 to 2, while one minute let me explain. so work is being given work and if
it comes back again to the state 1 then he has found out that some heat the work is being
given heat is coming out 2 to 1 and he has found out that this w1-2 is exactly equal
to Q2-1 and this is a cyclic process, what is a cyclic process? If a system performs
number of processes so that it comes back again to the initial state then the number
of processes forms a closed loop in thermodynamic diagram which is called a thermodynamic cycle.
So, it is a thermodynamic cycle or cyclic process where system starts from 1 goes to
2 and then system comes back again to two. But if it is not a reversible process, then
we can show it by a dotted line, you can ask me a question that, how do you specify the
process. This will be shown by a dotted line, that
means now I tell you that, when I specify a natural process in a thermodynamic diagram
it is always advisable you show it by a because this is a irreversible process not a quasi
equilibrium process by a w1-2 by a dotted line it you cannot specify it by a form line
and this is the process where heat is this is coming out to coming back to the initial
state.
So we get the work w2-1 and w1-2 is Q2-1 simply this was the observation of Joule. While we
did the experiment that time the unit switch were expressing the mechanical work and the
heat quantity were entirely different. Therefore, because of these difference in
unit, the work quantity evaluated in that unit and heat quantity evaluated in the unit
of heat that was previously existing calorie, these two are not equal and there was proportional
to each other which is known as mechanical equivalent of it, but that is absolute by
this time, because now work and heat are expressed in the same unit, because they are the same
type of energy transfer which can cause similar effects in a system and in a cyclic process
if you see then the work becomes equal to heat.
Now I describe this process, let this statement in a more formal way. Now, before doing that
I must do there are sign conventions.
Sign conventions implies write that sign convention of work and heat transfer of work and heat
flow now let us consider a system with respect to a closed system I am drawing it is same
for open system and work is coming out, it is considered positive. So positive direction
of the work is consist a convention you can do it in other way also but this is the convention
most of the books most of the literature follow this when work is coming out of the system
to surrounding we call it as positive. when work is given to the system from a surrounding
it is negative just delivers this the heat that means when heat is giving to the system
then heat is positive while heat is coming out of the system it is negative so common
convention which is going on since the birth of thermodynamics is this that the two different
directions are considered the positive for this two cases.
When work quantity is concerned work coming out of the system to the surrounding is considered,
positive work going into the system from the surrounding is negative, while it is the reverse.
When heat is given into the system is positive coming out is the negative, but you can do
other way also that means, positive for both the quantities in the same direction, the
work out is positive heat out is positive, work in is negative heat in is negative, but
this way you will be confused because most of the literature and the follows this terminology.
So, therefore the equations will be little different we get plus minus sign but ultimately
the results are same that you will see afterwards. Better we should follow this convention the
work coming out is positive coming out of a system and the reverse is the negative.
Similarly, heat given into the system is positive coming out is negative, so with this as the
sign convention and choose experiments in mind, now we can tell the thermodynamics first
law in a formal form like this.
The first law is the algebraic sum of work and heat interactions, net work and heat interactions
in a cyclic process by a system with its surroundings in a cyclic process is zero. Today it appears
to be a common sense, because in a cyclic process when a system come backs to its initial
state all the energy interactions have to be zero, it gains something, it loose something
and ultimately it is net zero. So, that it can come back to its initial state,
this is the formal statement of the first law of thermodynamics the algebraic sum of
net heat and work interactions between a system and its surrounding in a thermodynamic cycle
is zero, that means, with this definition we can write that algebraic sum of heat in
a cycle is equal to algebraic sum of with this sign convention positive to positive,
that means if there is a net heat added to the cycle then there will be a net work out
of the cycle has to be whose magnitude will be same as the net it added, that means net
interactions of heat and work will be zero.
so this is basically the first step of the analytical expressions of the first law of
thermodynamics This can be written like this, in an integral fashion and taking this into
this side Q minus w this means in a cycle with a sign like that the direction is equal
to zero, that means difference of heat and work interactions in a cyclic process must
be zero, Q minus w is zero. This can be interpreted in a different way
like this, if I write this for a small infinite small process in state of Q and W, let us
write this deltaQ minus deltaw the same expression I am writing what is this that means, we consider
an infinite small process executed by a system where deltaQ is the heat added and deltaW
is the work done by the system. That means, we consider a system which performs an infinite
small process, try to understand and a differential amount of heat differential means not in calculus
sense of differential because Q and W are the path function they cannot be differentiated,
that means infinite small amount of deltaQ is given and infinite small amount of deltaW
is coming out. If you integrate this in a thermodynamic cycle, then we can write cyclic
integral delQ minus delW is 0, why I am writing this way.
Now you know from mathematics elementary mathematics that cyclic integral of any point function
is zero, which means I can write cyclic integral of any point function x in this fashion dx
is zero x is any point function which is a property of a system
So, for any property of a system already in my knowledge I can write differential of that
property in a cyclic integral resident physical sense also tells like that in a cyclic integral
property change has to be zero because it comes back to its initial state, so all properties
will be regain back to its initial values, so property changes as zero, therefore for
all properties and all point functions x this is zero and if this is so then obviously one
can tell that this becomes is equal to dx, that means this difference can be expressed
by a point functions which he may not load so far .
But now we know that the difference between the heat and work is a point function, note
in a cyclic process that means, in an infinite small process deltaQ minus deltaW is dx. That
means we have recognized deltaQ is the heat given to a system in a infinite small process
and we get the work done as deltaW, but their difference we don't know what it is,it will
be something, but its cyclic integral is zero, but now at least to you know that their difference
is a point function that means if you convert the statement to a finite process then you
can write Q minus W is delta of x, x is the property.
That means for any finite process the heat given to the system in executing the process
minus the work delivered by the system in executing the process is equals to the change
of a point function that means heat is a path function, work is a path function; but their
difference is a change in a point function. We go to the earlier one which we discussed
that there are number of paths connecting the two state points work and heats are different,
but their differences are same that means they are different but following a constant
in equations that difference between this two Q and W though Q and W are varying from
process to process, but their difference is the same that means this is the change of
a point function between the two states and this point function is defined as internal
energy s. So, therefore now we can write, for an infinite small process deltaQ minus
deltaW is dE, now E as the internal energy well so this can be written this way sometimes
deltaQ taking this here deltaW plus dE now for a finite process what will be Q minus
W is equal to deltaE and this will be Q is equal to W plus deltaE.
Now, if we denote this state points then it will be much better, that means process connecting
one to two terms that means from state 1 to state 2 work obtained for the process from
state 1 to state 2, then delE from state 1 to state 2 will be simply E2 minus E1 that
means this version will be Q1-2 is equal to W1-2 plus E2 minus E1. Now, mathematically
this is arrived physically also it is true that in a system executing a finite process
if I give some amount of heat and if I take some amount of work their balance has to be
stored in the system. They are not necessarily make equal they not
necessarily to be equal they may be equal in that case dE will be zero but if they are
not equal then they are balance has to be stored in that, that means if heat added is
more than the work coming out then this is positive that means the difference will be
stored as an energy within the system. If it is other way some stored energy has to
be released so that there will be a decrease in the internal energy. So therefore this
gives the point function status of energy by thermodynamics which is defined as internal
energy and physically which we mean as energy stored in a system.
Now what is this internal energy? Now, I think that internal energy E composed of several
paths. The very first is that in any system what is the very primary form of internal
energy or fine primary component of internal energy which is stored in a system, intermolecular
energy because of temperature if in a based system does not move there is no kinetic energy
nothing that there is intermolecular energy. So, first part is the u which is inter molecular
energy, plus there may the other forms of energy stored any form of energy stored within
the system will be consider internal energy. I give you one example, that there is a gas
or there is a motion with in it that means the kinetic energy contained within the system
there may be kinetic energy plus there may be potential energy of the system because
of its position or placement in a conservative force filled that you place the system in
a conservative force filled the work done on it non dissipative work that is stored
within the system as the stored energy that is potential energy or any other kind of energy.
So, therefore the internal energy comprises of this, that means change of internal energy
all are point functions du plus d of KE plus d of PE plus d of any other form of stored
energy. All these together comprise the internal energy
E, so this is the form that internal energy is defined. So, therefore we see that internal
energy is a point function and we can define now internal energy like that.
A property of a system whose change in a process executed by the system equals to the difference
between the heat and work interactions by the system with its surrounding, this is another
form of first law, the beauty of first law is that though work and heat are path functions
but the difference is a point function two are path functions but their difference is
a point functions and that point function is the internal energy that is the energy
stored within the system. So, internal energy is therefore a property
of the system state variable which equals to the difference between work and heat and
another important point you must know the birth of internal energy or the definition
of the internal energy in classical thermodynamics is given through its difference, I am not
going to define internal energy on the absolute value, but it is initially defined in terms
of this difference, that means heat minus work is the difference in internal energy
not equals to the internal energy. Today I think I will end here. We have just started
the first law internal energy how the first law is written. About the sign convention
now you see the sign convention is that cyclic integral dQ minus dw is zero.
Some modern books you will see the cyclic integral dQ plus dw is 0, just all on a suddenly
open the book are we what professor. Stomads Tolds cyclic integral dQ minus dw is 0 and
dQ plus dw is 0, that means the sign convention is that there in same directions both are
positive very simple, but if you follow the classical sign convention that work coming
out is positive then heat given in the positive then cyclic integral dQ minus dw is 0 or delQ
minus delW this del and d are infinite small amount of work and heat interactions not their
differential, because they are path functions, but their difference is a point function which
is the differential of internal energy that is an exact differential because internal
energy the state variable and point function. When it is suddenly removed, this is a irreversible
works that has to be found out from the experiment that cannot given by these expression, but
one thing when I define the first law of thermodynamics, there is no restriction on friction because
it is the conservation of energy there is no restriction on friction
Now, if somebody once to substitute W by pdV then the question of friction comes in to
be there is a constant that it is a frictionless system reversible work you understand, so
in a irreversible work that means you suddenly reduce the load and the piston the cylinder
comes first and work is deliver to the surrounding that is an irreversible one that is to be
measured only given by the measured value that cannot be substituted by pdV work.
Now, Q is equal to W plus G it is for both frictional and frictionless systems so that
there is reversible work or irreversible work but when you substitute the work by some term
then you have to be causes what you are doing if you substitute it by pdV then you are doing
it for irreversible process that means non dissipative frictionless system, Otherwise
you are not permitted to do that that I will come afterwards all right any question
Paddle wheel work and shaft work is different, paddle wheel work is the work which is done
in a closed system by virtue of the friction if you rotate a stirrer rotate a paddle wheel
that is the work transfer and shaft work is different that is the rotation of a shaft
against the resistance against a torque that is also a non reversible work, but that is
a different kind of work which pertains to a control volume system continuous flow of
matter which gives rise to so we gives ah some amount of work transfer to the surrounding
through the rotation of the shaft that is the only difference.
We cannot make these two things in a same shape and try to find out a microscopic difference
between that these two things are entirely different, one part into a closed system and
the work done by rotating a paddle wheel by the agency friction another is an open system
where the work is developed by the rotation of a shaft against a resisting torque, that
is the difference just the difference as it is by the physics of the thing as you describe
it mechanically. There is no more thermodynamics in between this .Thank you.