Chapter 4 First Law of Thermodynamics - WNSO · 2011-07-20 · [R Gnyawali/P Timilsina] Page 1 Chapter 4: First Law of Thermodynamics Conservation Principles and the First law of

[R Gnyawali/P Timilsina] Page 1

Chapter 4: First Law of Thermodynamics

Conservation Principles and the First law of Thermodynamics So far, we have considered various forms of energy such as heat Q, work W, and total energy E individually, and no attempt is made to relate them to each other during a process. The first law of thermodynamics, also known as the conservation of energy principle, provides a sound basis for studying the relationships among the various forms of energy and energy interactions. Based on experimental observations, the first law of thermodynamics states that energy can be neither created nor destroyed during a process; it can only change forms. Therefore, every bit of energy should be accounted for during a process.

Energy cannot be created or destroyed; it can only change forms. The above figure depicts the law of energy conservation. Conservation Principles i) Principle of conservation of mass for closed System: Mass can’t be created or destroyed but may be converted from one chemical form to another. The mass of control mass (Closed System) system never changes.

dm = 0 m2 – m1 = 0 m2 = m1 i.e. m = constant

ii) Principle of Conservation of energy for Closed System: “A change in total energy of a control mass system (closed system) is equal to the net energy transfer to (or from) the system as heat and work”. [First Law of Thermodynamics for closed system].

Energy balance for closed systems: Change in energy = Net heat transfer to the system – Net work transfer from the system Mathematically;

dE = δQ – δw ……………………………….(1) The total energy (dE) is the sum of the internal, kinetic, and potential energy. Thus;

dU + d(KE) + d(PE) = δQ – δw


U2 – U1 + (KE2 – KE1) + (PE2 – PE1) = Q12 – W12

(U+KE+PE)2 – (U+KE+PE)1 = Q12 – W12 ………………………….(2)

In intensive terms;

The instantaneous time rate form of the energy balance equation is First law of thermodynamic for cyclic process undergoing closed system: “When a system undergoes a thermodynamics cycle then the net heat supplied to the system to the surroundings is equal to the net work done by the system on its surroundings”.

First law for cyclic Process, Proof: According First law; dE = δQ – δw If the control mass undergoes a complete cycle that takes the control mass from state 1 back to state 1. Therefore;

Hence, the first law of thermodynamics can also be stated as follows: If the system is carried through a cycle then the summation of the work delivered to the surroundings is equal to the summation of heat taken from the surroundings. Prove that “Total energy or internal energy is property of a System”. There exists a property of a closed system such that a change in its value is equal to the difference between heat supplied and the work done during the change of state.


Other Statements of First law of Thermodynamics 1) The internal energy of a closed system remains unchanged if the system is isolated from its surroundings. According to 1st law of thermodynamics;

This shows that the initial energy of the system is equivalent to final energy of the system. In other words, the energy of an isolated system remains constant. 2) A perpetual motion machine (PMM I) of the first kind is impossible. A PMM I deliver work continuous without any input. The only interaction with the surrounding is the delivery of work. It is a device which operates in a cycle. To have such a device is obviously impossible as it violates the first law of thermodynamics.

It means that there is no work output without any heat input. 3) Other statement is that an extensive property exists whose increment is equal to the work received by the system when closed system undergoes in adiabatic process.

For an adiabatic process, Q = 0 , so First law becomes as dE = – W

Therefore, the work is equal to the change in total energy for an adiabatic process. Internal Energy: This is defined as the sum of all the microscopic forms of energy of a system. Energy modes on the microscopic level such as energy associated with molecular binding, nuclear spin, molecular translation, molecular vibration, and the molecular activity of the constituent particles of the system. We are mostly concerned with the change in internal energy not absolute value of internal energy. This internal energy is proportional to temperature of the system.


Application of first law to some common Process 1) Reversible Constant Volume Process (V = constant) i.e. isochoric process


2) Reversible Constant Pressure Process (P = Constant) i.e. isobaric process

3) Reversible Constant Temperature Process( T=Constant) i.e. Isothermal Process


4) Reversible Adiabatic Process

Relation between T and V, T and P in Adiabatic Process:


5) Polytropic Process (PVn = Constant)


First Law of Thermodynamics for a Control Volume (Open System) (Control Volume Formulation ): Although devices such as turbines, pumps, and compressors through which mass flows can be analyzed in principle by studying a particular quantity of matter, as it passes through the device, it is normally simpler to adopt the control volume point of view. A control volume is a region in space studied in a particular analysis. The surface that bounds the control volume may be called a boundary or a control surface. The boundary, which is defined relative to a specified coordinate frame may be fixed or may deform. Mass and energy may cross the boundary. As in the case of a closed system, energy transfer can occur by means of work and heat. In addition, another type of energy transfer must be accounted for: the energy accompanying mass as it enters or exits. Conservation of Mass for Control Volume: The conservation of mass principle for a control volume can be expressed as: “The change of mass within a control volume is equal to the mass entering minus the mass leaving”.


This is conservation of mass equation within Control Volume System.

Conservation of Energy for Control Volume System The mass flowing into the control volume carries energy with it, and the same is true for the outlets from the control volume. The net gain in energy from the inlets and outlets must equal the change in energy within the control volume plus the heat transfer minus the work done. The work term requires special attention since the fluid moving into and out of the control volume is doing work. The conservation of energy principle applied to a control volume states that “The change in energy within the control volume is equal to the net energy transported to the control volume plus the heat added minus the work done by the control volume”.


The rate of work done in the control volume formulation is the sum of the shaft and flow work.

Control Volume Analysis: The analysis of a system requires detailed consideration of the inlets and outlets to the control volume as well as the state within the control volume. Uniform properties are spatially constant but may vary with time. At inlets and outlets this means that the state across the crossing boundary is described by at any time by single values of the properties. Uniform properties within the control volume indicate that all elements within the control volume have the same value for the properties at any time. Non-uniform properties vary spatially. The time variation must also be addressed at the inlets and outlets as well as within the control volume. Steady state conditions at the inlets and outlets mean that there is no variation of the properties with time. The density, velocity, specific internal energy, etc. have constant values for all times. Steady state properties within the control volume indicate that there is no accumulation within the control volume that causes the properties within the control volume to vary with time.


Unsteady state conditions imply time variation either at the inlets and outlets or within the control volume. In summary, uniform and non-uniform describe the spatial variation while steady state and unsteady state describes the time variation. Steady state Process A steady state process is characterized by following features:

a. The control volume does not move relative to the coordinate frame. b. The state of the mass at each point in the control volume does not vary with time. c. The mass flow across the control surface does not vary with time (steady flow). d. The rates at which heat and work interact with the control surface does not change with time.

This condition permits consideration of the steady state operation where no mass or energy accumulates within the control volume. Thus;

Conservation of Energy for Control volume:

This is required energy balance equation for steady state control volume system.


Control Volume Applications: Steady-State Work Applications: Turbines, compressors, pumps and fans are typical steady state devices that have a work interaction with the surroundings. These devices generally have a single inlet and a single outlet. Also the change in potential energy from inlet to outlet is usually very small. Thus conservation equations reduce to:

The figures are examples of the steady-state work application.

Note: for adiabatic device or insulating wall, the heat transfer is equal to the zero. Turbine: A turbine is a rotary steady state machine whose purpose is to produce shaft work (power) at the expense of the pressure (and/or kinetic energy) of the working fluid.


For adiabatic Turbine, Q = 0. Compressor, Fan and Pump requires work input.

Conservation of Energy;

Since, compressor, Fan and pump has negative work (i.e. work input) If the compressor, fan and Pump is adiabatic wall or insulating wall, then

=0, Therefore, Conservation of energy becomes;

Steady State Flow Applications: Heat exchangers, condensers, steam generators, diffusers, and nozzles, throttling valves, and pipes are devices that operate at steady state and do not produce or consume work. Most experience very small changes in potential energy, so:

Heat Exchangers: A heat exchanger is used to transfer energy from on fluid to another. There is no work interaction with the surroundings, and the changes in potential and kinetic energies are typically small.


A condenser circulates cold water to condense a high-quality mixture to the liquid state.

Steam Generators (Boiler): A steam generator uses an energy source such as the burning pulverized fuel or a nuclear reactor to create a high-temperature fluid. There is heat transfer from this fluid to water which passes through tube banks to from a superheated vapor. Change in potential energy is negligible.

Diffusers and nozzles are used to control the velocity of the fluid. Diffuser decreases the velocity while increasing the pressure, and the opposite is true for a nozzle. A nozzle is a steady state device whose purpose is to create a high-velocity fluid stream at the expense of fluid’s pressure. These devices are simply area changing devices, as shown in Figure.


For Adiabatic Nozzle or Adiabatic Diffuser, The heat transfer is taken as zero. Then, Energy equation further becomes as:

Throttling valve: A throttling process occurs when a fluid flowing in a line suddenly encounters a restriction in the flow passage. The result of this restriction is an abrupt pressure drop in the fluid. There is typically some increase in velocity in a throttle, but both inlet and exit kinetic energies are usually small enough to be neglected.

This shows that in throttling process the enthalpy of system remains constant. Simple Pipe:

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Chapter 4 First Law of Thermodynamics - WNSO · 2011-07-20 · [R Gnyawali/P Timilsina] Page 1 Chapter 4: First Law of Thermodynamics Conservation Principles and the First law of