THERMODYNAMICS  THEORY



Path Function and Point Function

Path Function and Point Function


Path function and Point function are introduced to identify
the variables of thermodynamics.
 Path function: Their magnitudes depend on the path followed during
a process as well as the end states. Work (W), heat (Q) are path functions.
Process A: W_{A}_{} = 10 kJ^{}
Process b: W_{B}_{} = 7 kJ
 Point Function: They depend on the state only, and not on how a system
reaches that state. All properties are point functions.
Process A: V_{2}  V_{1} = 3 m^{3}
Process B: V_{2}  V_{1} = 3 m^{3}



Heat



Heat is energy transferred from one
system to another solely by reason of a temperature difference between
the systems.
Heat exists only as it crosses the boundary of a system and the direction
of heat transfer is from higher temperature to lower temperature.
For thermodynamics sign convention, heat transferred to
a system is positive; Heat transferred from a system is negative.
The heat needed to raise a object's temperature from
T_{1 }to T_{2 }is:
Q = c_{p} m
(T_{2 } T_{1})
where
c_{p} = specific heat of the
object (will be introduced
in the following section)
m = mass of the object
Unit of heat is the amount of heat required to cause
a unit rise in temperature of a unit mass of water at atmospheric pressure.
 Btu: Raise the temperature of 1 lb of water 1 ^{o}F
 Cal: Raise the temperature of 1 gram of water 1 ^{o}C
J is the unit for heat in the S.I. unit
system. The relation between Cal and J is
1 Cal = 4.184 J
Notation used in this book for heat transfer:
 Q : total heat transfer
 : the
rate of heat transfer (the amount of heat transferred per unit
time)
 δQ: the differential amounts of
heat
 q: heat transfer per unit mass



Modes of Heat Transfer



Conduction: Heat transferred
between two bodies in direct contact.
Fourier's law:
If a bar of length L was put between a hot object T_{H}
and a cold object T_{L} , the heat transfer rate is:
where
k_{t }= Thermal conductivity
of the bar
A = The area normal to the direction
of heat
transfer

Convection 

Convection: Heat transfer between a solid
surface and an adjacent gas or liquid. It is the combination of conduction
and flow motion. Heat transferred from a solid surface to a liquid
adjacent is conduction. And then heat is brought away by the flow
motion.
Newton's law of cooling:
where
h_{} = Convection heat transfer
coefficient
T_{s}_{} = Temperature
of the solid surface
T_{f}_{} = Temperature
of the fluid
The atmospheric air motion is a case of convection. In
winter, heat conducted from deep ground to the surface by conduction.
The motion of air brings the heat from the ground surface to the high
air. 
Radiation 

Radiation: The energy emitted by matter
in the form of electromagnetic waves as a result of the changes in the
electronic configurations of the atoms or molecules.
Stefan  Boltzmann law:
where
σ = Stefan 
Boltzmann constant
ε = emissivity
T_{s}_{} = Surface
temperature of the object
Solar energy applications mainly use radiation
energy
from the Sun.



The three modes of heat transfer always
exist simultaneously. For example, the heat transfer associated with
double pane windows are:
 Conduction: Hotter (cooler) air outside each pane causes conduction
through solid glass.
 Convection: Air between the panes carries heat from hotter pane
to cooler pane.
 Radiation: Sunlight radiation passes through glass to be absorbed
on other side.
Please view heat transfer books for details of modes
of heat transfer.



Work

Definition of Work
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to View Movie (48 kB) 

Work is the energy transfer associated with a force
acting through a distance.
Dot product means the distance along the force's direction. For example,
if a car runs at a flat road, its weight does zero work because the weight
and the moving distance have a 90^{o }angle.
Like heat, Work is an energy interaction between a system
and its surroundings and associated with a process.
In thermodynamics sign convection, work transferred out
of a system is positive with respect to that system. Work transferred
in
is
negative.
Units of work is the same as the units of heat.
Notation:
 W : total work
 δW: differential amount of
work
 w: work per unit mass
 :
Power, the work per unit time



Expansion and Compression Work



A system without electrical,
magnetic, gravitational motion and surface tension effects is called
a
simple compressible system. Only two properties are needed to determine
a state of a simple compressible system.
Considering the gas enclosed in a pistoncylinder device
with a crosssectional area of the piston A.
Initial State:
 Pressure P_{1}
 Volume V_{1}
Finial State:
 Pressure P_{2}
 Volume V_{2}
Then a work between initial and final states is:
Pressure P, Volume V. Let the piston moving ds in a quasiequilibrium
manner. The differential work done during this process is:
δW = F
ds = P A ds = P dV
The total work done during the whole process (from state
(P_{1},V_{1}) to state (P_{2},V_{2}))
is:
This quasiequilibrium expansion process can be shown on a PV diagram. The differential area dA is equal to P dV. So the area under the process curve on a PV diagram
is equal, in magnitude, to the work done during a quasiequilibrium expansion or compression process of a closed system. 

