First Law of Thermodynamics (02 hours)Introduction FORMS OF ENERGYEnergy can exist in numerous forms such as thermal, mechanical, kinetic, potential, electric, magnetic, chemical, and nuclear, and their sum constitutes the total energy E of a system. The total energy of a system on a unit mass basis is denoted by e. E=me

Internal Energy UIn thermodynamic analysis, the total energy of a system in two groups: macroscopic and microscopic. The macroscopic forms of energy are those a system possesses as a whole with respect to some outside reference frame, such as kinetic and potential energies.The microscopic forms of energy are those related to the molecular structure of a system and the degree of the molecular activity, and they are independent of outside reference frames. The sum of all the microscopic forms of energy is called the internal energy of a system.

EnthalpyIn addition to the internal energy U, it is important to define another property called the enthalpy H.

Where On per unit mass, by It is defined by the relation:

The product pV is called the flow work. It represents the amount of work done by a substance as it flows in or out of a system to overcome the resistance at the entrance or exit.

Kinetic Energy KEThe energy that a system possesses as a result of its motion relative to some reference frame is called kinetic energy KE. When all parts of a system move with the same velocity, the kinetic energy is expressed asPotential Energy PEThe energy that a system possesses as a result of its elevation in a gravitational field is called potential energy PE and is expressed as Total Energy EThe total energy of a system consists of the kinetic, potential, and internal energies and is expressed as

E = PE + KE + U

HeatIn thermodynamics, heat is defined as a transfer of energy across the boundary of a thermodynamics system due to a temperature difference between the system and the surroundings.

Sign Convention

Q > 0: heat transfer to the systemQ < 0: heat transfer from the system

Work Work = Force Distance moved in the direction of force.

Unit: Nm (=Joule)

Sign Convention Work is done by the system is assumed as positive. On the other hand, if the work is done on the system is negative.

Some forms of energy and the associated work interactions

#Macroscopic form of energy Governing equationEnergy interaction WorkWork interactionBlock diagram

1. Kinetic Energy(translation) F dx

2.Kinetic energy(rotational) T d

3.Spring stored energy (translational) F dx

4.Spring stored energy (rotational) T d

5.Gravitational energy F dz

6.Electrical energy (capacitance) u dq

7.Electrical energy (inductance) i d

First law of thermodynamicsThe first law of thermodynamics, also known as the principle of conservation of energy, states that the energy can neither be created nor destroyed, it can only change forms. In other words, during an interaction between a system and its surroundings, the amount of energy gained by the system is exactly equal to the amount of energy lost by the surroundings.

When a system undergoes a thermodynamics cycle then the net heat supplied to the system from its surroundings is equal to the network done by the system on its surroundings. or

First Law of Thermodynamics for a Non-flow, Non-cyclic ProcessThe net algebraic sum of heat and work during a quasi-static process is equal to the change in internal energy during the same process.Mathematically

Corollaries of first law of thermodynamicsCorollary 1. There exists a property of a closed system such that a change in its value is equal to the sum of the net heat and work transfers during any change of state. (Concept of Internal energy from the 1ST Law)Proof:Let the system be taken from the state 1 to the state 2 by the two different processes 1a2 and 1b2 as shown in Figure.

Let us consider,Let the system be taken from state 2 to 1 through 2c1. Now the processes 1a2 and 2c1 together constitute a cycle.

Similarly, the processes 1f2 and 2c1 together constitute a cycle for which

If inequality (X) is true then equations (Y) and (Z) contradict each other which implies that these quantities must be equal. Therefore is the independent of the path. If the property is denoted by U,

The property U is called internal energy of the system.

Corollary 2. The internal energy of a closed system remains unchanged if the system is isolated from its surroundings.Proof: The first law of thermodynamics for any process can be written as

If the system is isolated, it exchanges neither mass nor energy with the surroundings

U = constantTherefore there is no change in the total energy within the system during the process.

Corollary 3. A perpetual motion machine of the first kind is impossible.Proof:An engine which could provide work transfer without heat transfer would violate the first law because it would create energy. So, an engine which could provide work transfer without heat transfer would run forever; in other words, it would have perpetual motion! Such an engine would have what is sometimes called perpetual motion of the fist kind.

It is always to devise a machine to deliver a limited quantity of work without requiring a source of energy in the surroundings. For example, a compressed gas in a pistoncylinder arrangement will expand and do work at the expense of the internal energy of the gas. Such devise cannot produce work continuously.

Non Flow and Flow Processes (02 hours)Introduction A process occurs when the system undergoes a change in a state or an energy transfer at a steady state. A process may be non-flow in which a fixed mass within the defined boundary is undergoing a change of state. Example: A substance which is being heated in a closed cylinder undergoes a non-flow process. Closed systems undergo non-flow processes.

A process may be a flow process in which mass is entering and leaving through the boundary of an open system. In a steady flow process, mass is crossing the boundary from surroundings at entry, and an equal mass is crossing the boundary at the exit so that the total mass of the system remains constant.

In an open system it is necessary to take account of the work delivered from the surroundings to the system at entry to cause the mass to enter, and also of the work delivered from the system at surroundings to cause the mass to leave, as well as any heat or work crossing the boundary of the system.Work and reversibility

Moving boundary work

Non flow energy equation and reversibilityThe reversible non-flow energy equation can be written as

For unit mass

Application of First Law to Non flow processes (or closed system)a. Reversible Constant Volume (or Isochoric) Process (v = constant)An isochoric process, also called an isometric process or an isovolumetric process, is a process that takes place at the constant volume.

From the First Law, For mass m of working substance

b. Reversible Constant Pressure (or Isobaric) Process (p = constant)

From the First Law, For mass m of working substance For mass m of working substance

c. Reversible Temperature (or Isothermal) Process ()In this case the gas or vapour may be heated at constant temperature and there shall be no change in internal energy. The work done will be equal to the amount of heat supplied, as shown ahead. For a perfect gas during isothermal process;

From the First Law,For mass m of working substance or

d. Polytropic Reversible Process Where n is the index which can vary from to + .

From the First Law,Also For mass m of working substance

The terms steady and uniform are used frequently in engineering. Steady implies no change with time. The opposite of steady is unsteady, or transient. Uniform implies no change with location over a specified region. Non Steady flow & Steady flow energy equation

Flow work Unlike closed systems, control volumes involve mass flow across their boundaries, and some work is required to push the mass into or out of the control volume. This work is known as the flow work, or flow energy, and is necessary for maintaining a continuous flow through a control volume. Before entering After enteringIf the fluid pressure is p and the cross-sectional area of the fluid element is A, The force applied on the fluid element by the imaginary piston To push the entire fluid element into the control volume, this force must act through a distance L. Thus, the work done in pushing the fluid element across the boundary (i.e., the flow work)

The flow work per unit mass is:

Total Energy of a Flowing FluidThe total energy of a non flowing fluid consists of three parts: internal, kinetic, and potential energies. The fluid entering or leaving a control volume possesses an additional form of energy (flow energy: pv). Then the total energy of a flowing fluid on a unit-mass basis becomes

Non-flowing fluidFlowing fluid

Kinetic energy

Potential energyPotential energyInternal energyKinetic energyFlow energy

Internal energy

Non-steady flow process

Entering Leaving Rate of internal energy Rate of displacement or flow work Rate of kinetic energy Role of potential energy Rate of energy of the fluid entering the system

Rate of energy of the fluid leaving the system

For a control volume undergoing any unsteady flow process, principle of conservation of energy can be expressed as

The unsteady flow energy equation (USFEE) in the rate form is

For a control volume undergoing any unsteady flow process, principle of conservation of mass can be expressed as

The unsteady flow mass equation (USFME) in the rate form is

Steady flow processWe can deduce the equations for steady flow from USFEE since the steady flow is a special case of unsteady flow.

Assumptions:The following assumptions are made in the system analysis:(i) The mass flow through the system remains constant (ii) Fluid is uniform in composition.(iii) The only interaction between the system and surroundings are work and heat.(iv)The state of fluid at any point remains constant with time.(v) In the analysis only potential, kinetic and flow energies are considered.

For a steady flow process

The steady flow energy equation (SFEE) in the rate form becomes

For a unit mass basis (dividing the equation by)

Open systems with steady flowBoiler: the fluid entering as a liquid and leaving as a vapour at a constant rate. In this case no work is done. W=0. KE at inlet and outlet are negligible since the velocities of flow are quite low. the steady flow energy equation can be reduced to

CondenserVapour passes over a bank of tubes, and is condensed as it comes into contact with the surface of the tubes. The tubes are maintained at a lower temperature than the vapour by a flow of cooling water. The cooling water is not part of the fluid of this open system but acts as a sink of heat in the surroundings.

Turbine:A turbine is a means of extracting work from a flow of fluid expanding from a high pressure to a low pressure. Turbines using gas as working fluid are called gas turbine where as turbines using steam are called steam turbines. Expansion in turbine is assumed to be of adiabatic type so that the maximum amount of work is produced.Assuming change in kinetic energy, potential energy to be negligible, and the process can be assumed to be adiabatic; the steady flow energy equation can be modified as

Compressor:The rotary compressor can be regarded as a reversed turbine, work being done on the fluid to raise its pressure. In this case work is done on the fluid by a bladed rotor driven from an external source. This increases the velocity of the fluid. The velocity is then reduced in a set of fixed diffusers to some value approximating to that at the inlet to the compressor, and the pressure is increased.

Nozzle Nozzle is a duct of varying cross-sectional area so designed that a drop in pressure from inlet to outlet accelerates the flow. The flow through a nozzle occurs at very high speed, and there is little time for fluid to gain or loose energy by a flow of heat through the walls of the nozzle as the fluid passes through it. The process is therefore always assumed to be adiabatic. Also, no work crosses the boundary.

Diffuser The function of a diffuser is the reverse of that of a nozzle; the diffuser is a duct so shaped that the fluid flowing through it decelerates, the pressure increasing from inlet to outlet.

Throttling A flow of fluid is said to be throttled when some restriction is placed in the flow. KE inlet and outlet can be negligible since it is a low speed flow. No heat transfer across the boundary. No work crosses the boundary. Thus the energy equation reduces to

, the process is an adiabatic steady-flow process such that the enthalpy is the same at inlet and outlet.

Mixing Chambers

Two or more fluid streams are mixed to form one single fluid stream.In the steady flow,Note that there is no shaft work in a mixing chamber, and the changes in kinetic and potential energies of the streams are usually neglected.For the conservation of mass across the mixing chamberMixing chambers are usually well insulated, so that the process can be treated as adiabatic.

Heat Exchangers

In the industries, there is often a need to cool a hot fluid stream before it is let out into the environment.There is no work transfer, and the changes in kinetic and potential energies are neglected In the steady flow,Note that there is no work transfer, and the changes in kinetic and potential energies are neglected.Where a heat exchanger is insulated, it is adiabatic and the heat transfer term may be neglected.

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