first law of thermodynamics

M Sc Engineering in Energy Systems
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First Law of Thermodynamics

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First Law of Thermodynamics
First law of thermodynamics is based on the conservation
principles.
It gives the mathematical expression for the effect of the
interactions between the system and surrounding on the stored
energy (total energy) of the system.
In closed system (control mass), interactions can take place only in
the form of energy transfer (work transfer and heat transfer).
Therefore first law of thermodynamics for a control mass can be
explained with reference to conservation of energy only.
Whereas in an open system (control volume), interactions can take
place both by the mass transfer and energy transfer. Hence the first
law of thermodynamic for a control volume is explained with
reference to both mass conservation and energy conservation
principles.
THERMO-FLUID ENGINEERING

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First Law of Thermodynamics for a Control Mass
Conservation of Mass for a Control Mass
Control mass (closed system) is a system in which energy transfer
can take place but mass transfer cannot. Hence, conservation of
mass for a control mass can be stated as
Total mass of a control mass always remains constant.
For any process between state 1 and 2,
In terms rate

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Conservation of Energy for a Control Mass
The change in total energy of a control mass is equal to the heat
supplied to the control mass minus the work produced by the
control mass.
In terms rate
For any process 1-2 between state 1 and 2,

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Substituting expression for total energy
It can also be rearranged for the heat transfer as
Most common example of a control mass is a piston cylinder
device and for a stationary piston cylinder device the changes in
potential energy and kinetic energy are negligible in comparison to
the change in internal energy. Therefore, for the piston cylinder
devices,

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Conservation of Energy for a Control Mass Undergoing a
Cycle
A process is said to be a cyclic process, if the initial state of the
system is restored by a number of different processes in series. For a
cyclic process, initial and final states are identical.

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Whenever a control mass is
taken through a cycle then the
heat transferred to the control
mass is equal to the net work
done by the control mass.
Taking cyclic integral
For a cyclic process,
Then the above equation reduces to
It can also be expressed in the equivalent form as
Whenever a control mass is
taken through a cycle then the
heat rejected by the control
mass is equal to the net work
done on the control mass.
OR

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First Law of Thermodynamics for a Control Volume
Conservation of Mass for a Control Volume
Any control volume (open system) can interact with its
surroundings by energy as well as mass transfer. Hence,
conservation of mass for a control volume can be stated as
The change in mass within a control volume is equal to the
mass entering into the control volume minus the mass leaving
the control volume.
where,

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Expression for Mass Flow Rate
Total mass of the fluid crossing the section of length L is given by
The mass flow rate is then given by

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Conservation of Energy for a Control Volume
Along with heat transfer and work transfer, mass transfer also affects
the total energy of a control volume. Mass entering into the control
volume increases the total energy of the system where as mass
leaving from the control volume decreases the total energy of the
system. Hence conservation of energy for a control volume can be
stated as:
The change in total energy of a control volume is equal to the net
energy transported by the fluid into the control volume plus the
heat transferred to the control volume minus the work done by
the control volume.
where

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Heat transfer always occurs due to the
difference in temperature between the
system and the surroundings whether
it’s a control mass or control volume,
i.e.,
But the total work transfer associated with a control volume includes
various modes of work transfer such as flow work, shaft work,
expansion/compression work, etc, i.e.,
Energy (work) required for the displacement
of the fluid is given as
Specific flow work or flow work per unit mass of the flowing fluid

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Therefore, the rate of flow work is evaluated as
Then general expression for the total work transfer is given by
where
Then general energy equation for the control volume reduces to

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Substituting h = u+ Pv,
Control Volume Analysis
While analyzing a control volume with reference to time, it can be
classified as a steady state system or an unsteady state system. If the
properties of the system at a particular point do not vary with time, it
is called a steady state system and if the properties of the system at a
particular point vary with time it is called an unsteady state system.
Steady State Analysis
For the steady state operation of a control volume, its properties
(total mass and total energy) should not change with time.

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Most common examples of steady state devices are turbine,
compressor, nozzle, etc. These devices have single inlet and single
outlet. If we denote inlet section by 1 and outlet section by 2, i.e.,
Energy equation reduces to

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Unsteady State Analysis
During the unsteady state operation of a control volume, its
properties (total mass and total energy) change with time, i.e., total
mass and total energy of the system is function of time.
Integrating mass conservation equation

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Integrating energy conservation equation

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Control Volume Applications
Depending upon their operation and function, common control
volume applications can be classified into four groups: steady state
work applications, steady state flow applications, unsteady state
work applications and unsteady state flow applications.
Devices which operate under steady state conditions and either
produce or consume work are called steady state work applications.
Common examples of steady state work applications are turbine,
compressor, pump, fan, etc.
Steady State Work Applications

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Turbine
A turbine is a device which produces power by consuming energy
carried by a fluid. A turbine has generally a single inlet and a single
outlet, therefore energy equation for the steady state operation of the
turbine is given as
If turbine surface is insulated and heat transfer
loss is negligible, it is called an adiabatic
turbine. Therefore, for an adiabatic turbine
energy equation reduces to

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Compressor, Pump and Fan
Compressor, pump and fan increase fluid energy by consuming
mechanical work.
Compressor usually increases pressure energy of the gaseous
substance, pump increases pressure or potential energy of the liquid
substance and fan increases kinetic energy (by increasing velocity) of
the fluid. Hence energy equations for these devices are also given by
If these devices operate under the adiabatic
condition, energy equation is given by

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Steady State Flow Applications
Devices which operate under steady state conditions and do not
produce or consume work are called steady state flow applications.
Common examples of steady state flow applications are nozzle,
diffuser, heat exchanger, evaporator, condenser, throttling valve, etc.
Nozzle and Diffuser
Nozzle is a device with decreasing cross sectional area and is used to
increase fluid velocity where as diffuser is a device with increasing
cross sectional area and is used to decrease fluid velocity. These
devices have a single inlet and a single outlet and therefore general
energy equation for these devices is given as
If the nozzle or diffuser is operating under
adiabatic condition energy equation reduces
to THERMO-FLUID ENGINEERING

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Heat exchanger
Heat exchanger is a device used to transfer heat from one fluid to
another.
The energy equation for the control
volume is given as
The energy equation for control
volume is given as
Evaporator and Condenser
Evaporator converts liquid into vapor
by absorbing heat from the
surroundings whereas condenser
converts vapor into liquid by rejecting
heat to the surroundings.

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Throttling valve
Throttling valve reduces pressure of the fluid without performing
work. Heat transfer, change in potential energy and kinetic energy are
also negligible.
Energy equation for the throttling valve is given as

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Unsteady State Work Applications
Mass conservation and energy
conservation equations for the device are
given as
In case of piston cylinder device, changes in potential energy and
kinetic energy are negligible in comparison to change in internal
energy.

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Unsteady State Flow Applications
Mass conservation and energy
conservation equations for the device are
given as
In this case also, changes in potential energy and kinetic energy are
negligible in comparison to change in internal energy.

first law of thermodynamics

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