Prof' Vinod Kallur

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Prof. Vinod Kallur Chemical Engineering
Department R V College of Engineering, Bangalore
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In the previous session

• First law was applied to flow processes
• Solved numerical problems and discussed some VTU
  exam questions.

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In this session

• We will discuss p-V-T behavior of pure fluids
• State ideal gas law
• We will apply first law to various processes such
  as isochoric, isobaric, adiabatic and polytropic
  processes.

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Pressure, Temperature and volume of gases vary
in a definite manner.
Matter can exist in solid, liquid or gas phase
based upon the Pressure and Temperature
This information is best given graphically
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p-T diagram for pure substance (water)
Fluid
Critical Point.
Liquid
p
Solid
Gas
Vapor
T
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p-T diagram for pure substance (water)
Dashed lines do not represent phase transition.
Fluid
Critical Point.
Liquid
Phase is considered liquid if it can be vaporized
by reduction in pressure keeping T constant
p
Solid
Gas
Vapor
Phase is considered gas if it can be condensed by
reduction in T keeping p constant.
T
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p-T diagram for pure substance (water)
Gas that can be condensed either by compression
at constant T or by cooling at constant p is
called vapor
Fluid
C
Liquid
p
Solid
Gas
Vapor
T
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p-V diagram for pure substance
S / L
fluid
C
pC
L
S
Gas
pressure
L / V
V
TC
S / V
VC
Volume
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p-V diagram for pure substance

• Saturated liquid
• Liquid in equilibrium with vapor
• Saturated vapor

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fluid
C
pC
L
pressure
Gas
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L / V
V
TC
T1
VC
Volume
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p-V diagram for pure substance
Isotherm TC has a point of inflexion at the
critical point
C
pC
L
Gas
pressure
Mathematical representation?
L / V
V
TC
T1
VC
Volume
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Ideal gas
Internal energy is a function of temperature
only.
No matter what process, the changes in internal
energy and enthalpy are given by the above
expression not only for ideal gases even for real
gases.
For real gases heat capacity may be function of
p, V and T.
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Mathematically it is the simplest equation of
state.
No gas confirms to this equation for all values
of T and p.
However, this law is valid for low pressures,
large volume and low temperatures.
At constant pressure
At constant volume
Ideal gas undergoing various processes
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Isochoric process
Any process in which volume of the system does
not change is called isochoric process.
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Isobaric process
Since it is constant pressure process,
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Relation between CP and CV
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Isothermal Process
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Isothermal Process
Adiabatic Process
There is no heat exchange.
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Adiabatic Process
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Adiabatic Process
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Adiabatic Process
Temperature and volume changes in adiabatic
processes are related by this equation.
For adiabatic process pressure, volume and
temperature all change.
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Adiabatic Process
Work done
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We used the expression for internal energy to get
the expression for work done.
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Polytropic process
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Generally n lies between 1 and ?.
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Let us recapitulate what we did in this session

• p-V-T behavior of pure fluids
• Ideal gas law
• Isochoric, isobaric, adiabatic and polytropic
  processes.

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In the next session we will

• look into other equations of state
• Solve numerical problems.