Applications of First Law of Thermodynamics
First law of thermodynamics when it is applied to an open system has got
tremendous applications all across industries. Using this law you can
predict how much is the pressure drop across the nozzle, or how much is
the energy required by the pump to pump the fluid out, or what is the
heat transfer in heat exchanger, or what is the amount of work produced
by the turbine.
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| Fig.1 Industrial applications of first law of thermodynamics for an open system |
In a nutshell first law simply means conservation of energy, or it
states that energy is getting transformed from one form to another form.
First Law for Closed System
We will understand how first law is applied for a thermodynamic system
by analyzing a simple example, an example of piston cylinder
arrangement. Here the cylinder has got some gas inside it. Assume there
is no air leakage to the surrounding. So this is an example of closed
system where mass does not change. Assume the gas is absorbing some heat
Q from the surrounding; also assume that this gas is able to push the
piston upwards due to high pressure of gas. So the gas is doing some
work on the piston with quantity W.
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| Fig.2 Piston-cylinder arrangement to demonstrate first law for a closed system |
So there are 2 energy interactions to the gas, it will increase by a
quantity Q, because it is absorbing energy. And it will decrease by a
quantity W since it is losing energy by doing some work. So you can
write change in energy (E) of gas as follows.
This is first law of thermodynamics for a closed system. Same equation
you can write in differential form as follows. It is in form of rate of
change of quantities per unit time.
First Law for an Open System
Now we are going to open the system, or open the cylinder as shown below.
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| Fig.3 A piston-cylinder open system made by making the cylinder open |
The system is no more closed now, it’s an open system. The mass is
continuously varying. It can have an inlet mass flow rate at particular
pressure and particular velocity. Similarly there will be exit flow rate
of particular pressure and velocity. Here also our objective is the
same. We want to find out energy change of the gas or the system. But
here it is not possible to pin point a particular quantity of gas. The
gas is continuously flowing. So before proceeding to the energy change
calculation, we have to define a system first, a control volume where
you will do energy balance.
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| Fig.4 Defining a control volume for energy balance |
Here the dotted line represents the control volume, or the space at
which we will do energy balance. Here you can see there are 4 energy
interactions to the system. 2 energy interactions which are coming to
the system and another 2 energy interactions which leave the system. So
if you want to find out energy change in system you should add energy
transfer due to heat flow and inlet mass flow and subtract energy
transfer due to work done and exit mass flow. So for an open system
change in energy will be as follows.
Note that the flow stream has got 3 components of energy. Internal
energy, kinetic energy and potential energy. Z represents the altitude
of flow stream. This equation is the first law of thermodynamics for an
open system.
Concept of Flow work & Enthalpy – More Useful Form of First Law
But for an open system the term W, work done by the gas should be
carefully examined. Here the gas is doing work to push the cylinder up,
plus it is doing work to suck the fluid in or eject the fluid out. Or to
maintain the flow gas has to do some work. This kind of work, the work
which is required to maintain the flow is known as flow work. So the
total work done by the system will be summation of visible work and flow
work.
Wcv represents the visible work, in this case the work done by the gas
on the piston. And we know flow work is the work required to eject the
fluid out or suck the fluid out. The work required to eject the fluid
out will be force at exit portion multiplied by velocity of this stream.
Force is same as pressure at that portion times area. So we can
represent flow work like this.
If you do some rearrangement to the equation by substituting volumetric
flow rate as mass flow rate into specific volume, by representing u+Pv
as a new property enthalpy,
the above equation will be simplified like this.
This is the final and most useful form of first law of thermodynamics for an open system.
One Application of First Law
We will work out one interesting example using firs law equation in this
section. A pump problem, where fluid is getting pumped from point 1 to
point 2.
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| Fig.5 Work required by the pump for pumping fluid from state 1 to 2 is to be calculated |
We want to find out what’s the energy required by the pump to perform
this action. To find out that we will use equation derived for first law
of thermodynamics for an open system.We can assume the pump operation
is in steady state. So energy of the pump does not change with time. So
you can put first term in equation as zero. And usually there will not
be any heat transfer to the pump. So you can put that term also as
zero.
If cross sectional areas of point 1 and point 2 are equal, then
velocities will be equal, so from this equation velocity part also get
cancelled out. You can also assume height difference between inlet and
outlets are negligible. So the altitude term also gets cancelled out.
And finally what remains is this.
Work done by the control volume is mass flow rate times change in
enthalpy. If you want work done on control volume or energy required by
the pump, you have to just reverse the sign.
Using the same approach you can solve lot of other energy transfer problems in industries.
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