We were discussing various basic concepts of thermodynamics
such as thermal energy reservoir in thermodynamics in our recent post. We have
also discussed the concept of specific heat and enthalpy in the field of
thermal engineering.
Today we will prove that energy is a point function
and also a property of the system.
System energy is a point function and a property of the system, let us prove this statement
Before going ahead, we will just brief here the
concept of first law of thermodynamics. As we have already discussed that first law of thermodynamics deals with
the law of conservation of energy and according to law of conservation of
energy, energy can’t be created or destroyed but also it could be converted
from one form of energy to another form of energy.
We can also say that energy will always be
conserved. Heat and work, these are two different forms of energy. If heat
energy is provided to the system by the surrounding then system may provide the
work energy to the surrounding and similarly if work is being done upon the
system then system may deliver the energy in terms of heat to the surrounding.
Hence, this is the basic concept of first law of
thermodynamics. Now we will see here the detailed explanation behind the statement
that energy as property of the system and as point function too. After that, in
our next post, we will see first law of thermodynamics for an open system or control volume.
Let us assume that we have one system which is
undergoing a change of state from initial state 1 to another state 2 via
following the path A as shown in following figure. System is returning to
initial state i.e. state 1 from state 2 via following the path B. Here, we can
say that system is undergoing in a cycle 1-2-1 as displayed in figure.
Let us recall the “first law of thermodynamics for a system undergoing a change of state”
and apply for path A, where system is changing its state from state 1 to state
2. We will have following equation
QA-
WA= ∆EA
Similarly, we will have following equation when
system is changing its state from state 2 to state 1 via following the path B.
QB-
WB= ∆EB
We have already seen that system is undergoing in a
cycle 1-2-1 as displayed in above figure. Hence, we will use the concept of “first law of thermodynamics for a system undergoing a cycle”. Let us see the equation for system which constitutes a
cycle 1-2-1 and we will have following equation.
WA+WB=
QA+QB
WB-
QB = QA- WA
-
(QB- WB) = QA- WA
-
(∆EB) = ∆EA
Let us assume that system is returning to initial
state 1 from state 2 via following the path C, in that case we will go ahead similarly
as we have gone above and finally we will have following equation
-
(∆EC) = ∆EA
Now if we will look the end result for first case
where system is returning to initial state by following the path B and of
second case where system is returning to initial state by following the path C,
what we will secure here that change in system energy is same in both cases and
it will not depend over the path followed by the system to return to its
initial state.
Therefore we can conclude that system energy will
have some definite magnitude for each state of the system and it will not
depend over the path followed by the system and hence energy will be considered
as a point function and also a property of the system.
We will see another topic in our next post i.e.
You must find out and read the following quite useful engineering articles and these are as mentioned below.
Do you have suggestions? Please write in comment box
Reference:
Engineering thermodynamics by P.K. Nag
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