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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