First law of Thermodynamics open system [Mechanical engineering]

First law of Thermodynamics open system

First Law of Thermodynamics for an Open System

First Law for an Open System

Now we are going to open the system, or open the cylinder as shown below.

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.

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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FAQ

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What is the first law of thermodynamics?


Isolated: when it cannot exchange energy or matter with the surroundings.
Closed: when it can exchange energy but NOT matter with the surroundings.
Open: when it can exchange both matter AND energy with the surroundings.

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