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Friday, 29 July 2016

FIRST LAW OF THERMODYNAMICS FOR AN OPEN SYSTEM OR CONTROL VOLUME

We were discussing the concept of control volume system and concept of enthalpy in the field of thermal engineering in our previous posts, where we have seen the fundamentals of a control volume system as well as the specific heat and types of specific heat also.

Let us go ahead to discuss the application of first law of thermodynamics for an open system. First law of thermodynamics for an open system will be quite important for various industrial applications such as in fluid pumping unit.

We will be able to determine the required energy by a pump in order to pump the fluid at given head. We will have an idea of heat transfer in a heat exchanger or required work energy by air compressor in order to compress the atmospheric air up to a desired pressure once we will study thoroughly the first law of thermodynamics for an open system.

So take one cup of tea and enjoy here the fundamental of first law of thermodynamics for an open system

We have already seen the concept of control volume system. Let us consider one control volume system as displayed here in following figure. Let us consider two sections, first section at the inlet of the control volume system and another at the outlet of the control volume as displayed in figure.
First law of thermodynamics for control volume or an open system
Let us consider here that control volume is receiving heat energy from surrounding and providing the work energy to the surrounding. As we know that fluid will enter the control volume system and will leave the control volume system continuously i.e. there will be continuous flow of material or fluid through the control volume and hence we will consider the energy interactions between system and surrounding with respect to time.

Therefore let us consider the following important data as mentioned here.

The rate of heat energy addition to the control volume = δQ/δt
The rate of work energy providing by control volume to the surrounding = δW/δt.
The mass flow rate entering to the control volume = dm1/dt
The mass flow rate leaving the control volume =dm2/dt
Rate of change of mass in control volume = dmCV/dt

According to principle of conservation of mass, we will have following equation

(Mass flow rate entering to the system) - (Mass flow rate leaving the system) = Rate of change of mass in control volume
(dm1/dt) - (dm2/dt) = dmCV/dt

Conservation of energy

Let us consider the rate of change of internal energy of control volume is dECV/dt. Now , we will have to consider net energy entering to the control volume and net energy leaving the control volume as after securing above two data we will be able to secure the rate of change of internal energy of control volume i.e. dECV/dt.

As we are concentrated here on an open system, hence we will have to consider each form of energy associated with material flowing in and flowing out of the control volume apart from work energy and heat energy.

Let us first try to find out the various forms of energy those will be associated with the material flowing in to the control volume and flowing out from the control volume.

Energy associated with material or fluid flowing in to the control volume (or leaving the control volume) will be given by the summation of internal energy, pressure energy, kinetic energy and potential energy. 
Where E will be energy associated per unit mass.
E = u + pv + V2/2 + gz
E = h + V2/2 + gz
Ein = hin + V2in/2 + gzin = h1 + V21/2 + gz1
E1 = h1 + V21/2 + gz1
Similarly, energy associated with material or fluid leaving the control volume will be given as
Eout = hout + V2out/2 + gzout = h2 + V22/2 + gz2
E2 = h2 + V22/2 + gz2

So let us recall the statement of conservation of energy and write here the equation

Rate of change of internal energy of control volume = (Net energy entering to the control volume) – (Net energy leaving the control volume)

dECV/dt = (dm1/dt) E1 + δQ/δt – (dm2/δt)E2 - δW/δt

dECV/dt = (dm1/dt ) (h1 + V21/2 + gz1) + δQ/δt – (dm2/dt)( h2 + V22/2 + gz2) - δW/δt

We can also write this equation as mentioned here
We will come again with new topic "Heat engine in thermodynamics"in our next post.
Do you have suggestions? Please write in comment box.

Reference:

Engineering thermodynamics by P. K. Nag
Basic thermodynamics by Prof. S.K. Som
Image courtesy: Google

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