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: WA = 10 kJ
Process b: WB = 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: V2 - V1 = 3 m3
Process B: V2 - V1 = 3 m3
Heat is energy transferred from one
system to another solely by reason of a temperature difference between
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
T1 to T2 is:
Q = cp m
(T2 - T1)
cp = 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 oF
- Cal: Raise the temperature of 1 gram of water 1 oC
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
- δQ: the differential amounts of
- q: heat transfer per unit mass
||Modes of Heat Transfer
Conduction: Heat transferred
between two bodies in direct contact.
If a bar of length L was put between a hot object TH
and a cold object TL , the heat transfer rate is:
kt = Thermal conductivity
of the bar
A = The area normal to the direction
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
Newton's law of cooling:
h = Convection heat transfer
Ts = Temperature
of the solid surface
Tf = 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
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:
σ = Stefan -
ε = emissivity
Ts = Surface
temperature of the object
Solar energy applications mainly use radiation
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.
Definition of Work
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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 90o 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
Units of work is the same as the units of heat.
- W : total work
- δW: differential amount of
- 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
simple compressible system. Only two properties are needed to determine
a state of a simple compressible system.
Considering the gas enclosed in a piston-cylinder device
with a cross-sectional area of the piston A.
Then a work between initial and final states is:
Pressure P, Volume V. Let the piston moving ds in a quasi-equilibrium
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
(P1,V1) to state (P2,V2))
This quasi-equilibrium expansion process can be shown on a P-V diagram. The differential area dA is equal to P dV. So the area under the process curve on a P-V diagram
is equal, in magnitude, to the work done during a quasi-equilibrium expansion or compression process of a closed system.