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Sunday, 21 August 2016

PROVE THAT INTERNAL ENERGY IS A PROPERTY OF THE SYSTEM

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. What is internal energy in thermodynamics?
Do you have suggestions? Please write in comment box

Reference:

Engineering thermodynamics by P.K. Nag
Image courtesy: Google

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