1. Work and heat transfer
-ppt-2
Engg Thermodynamics-ME2102
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Presented by,
Lalitha P
Asst. Professor
Mechanical Engg.
RGUKT Basar
2. Introduction
• A system and its surroundings can interact in two ways:
i. by work transfer, and
ii. by heat transfer
• These may be called energy interactions and these bring about
changes in the properties.
• TD mainly studies these energy interactions and the associated
property changes of the system.
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3. Path functions
• Process functions
• a quantity that is well defined
so as to describe the path of a
process through the equilibrium
state space of a TD s/m.
• Depends upon the path history.
Ie., defined to describe the path
of a process.
• Eg: work, heat: dW, dQ, etc.
Point functions
• State functions
• a variable each value of which
is associated with and
determined by the position of
some point in space.
• Does not vary with the path
history. i.e., defined by the
state variables.
• Eg: TD state variables: dV,
dp,dT, etc.
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•These are inexact differential,
so with the symbol
•Energy in transit is path
function
•Eg: work transfer and heat
transfer
• These are exact differential, so
with the symbol
•Energy in storage is point
function
•Eg: internal energy
5. Work transfer
• Work is one of the basic mode of energy transfer, the action of a
force on a moving object is identified as work.
• Mechanical work is defined as, the work is done by a force as it
acts upon a body moving in the direction of the force.
• In TD, work transfer (W) is considered as occurring between the
s/m and the surroundings.
• Work is said to be done by a s/m if the sole effect on things
external to the system can be reduced to the raising of a weight.
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6. • Work transfer is a boundary phenomenon.
• When work is done by a system, it is arbitrarily taken to be
positive.
• And when work is done on a system, it is taken to be negative.
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Types of Work transfer
1. Displacement or pdV work transfer
2. Paddle wheel work
3. Flow work
4. Shaft work
1. Displacement or pdV - work transfer
• Due to displacement of the system boundary of a closed system.
8. • Piston is the only boundary which moves due to gas pressure.
• When piston moves out from the equilm state ‘1’ to ‘2’,
infinitesimal displaced distance is ‘dl’ due to the force ‘F’ acting
on the piston.
• Where, ‘F’ is the pressure force as ‘ F = p.A’ , here, ‘p’ is gass
pressure and ‘A’ is piston surface area.
• Then the infinitesimal work done by the gas on piston is
• i.e., dW = F.dl = (p.A).dl = p.(A.dl) = p.dV
• Hence,
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dW = pdV
9. • Therefore, total work done on the piston by the gas is
• Explanation:
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10. • For a process 1-2, if path is defined well then one can calculate
the work transfer the process.
• On the above diagram, a quasi-static process is assumed with a
definite path. It is shown on a p-V diagram, if dW = pdV, then the
area under the curve (quasi-static process 1-2) on a p-V diagram
gives the total work transfer.
• To calculate total W, take a strip under the curve with average
height ‘p’ and width ‘dV’ gives you the area of the strip as ‘pdV’.
i.e., dW = pdV. For the total area under the curve (total work
transfer), do the integration from the initial state limit to final
state limit. As the V is the variable on the work relation, apply the
limits as V1 and V2.
• Therefore, total work transferred during the process 1-2 is,
• Work is a path function so on the subscript of W ‘ path 1-2’ is mentioned.
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11. Displacement or pdV-work – contd…
• For a process 1-2, Work done can be calculated
as
• For a cyclic process, initial and final process are same, so change
in any property is zero.
• i.e., cyclic integral of any property is always zero.
• [so, for a cyclic process, work W can not be calculated as
Since, .]
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12. 2. Stirrer or paddle wheel work or stirring work
• Here, friction is the work transfer agent.
• Work is added to the system through the paddle wheel, due to
the paddle wheel rotation system molecules displaces rapidly as
the result of collision on the paddle wheel and also by colliding
each other. It increases the molecular friction, that leads to
increase in temperature further other properties of the system
change.
• It is a closed system process.
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14. • It is the work required to push a certain quantity of fluid across a
system.
• It is an open system process.
• To push ‘dm’ mass of fluid against the pressure ‘p’ exerted by the
system, external force ‘F’ will be applied.
• External force, F = p.A
so, work transfer W = F.dx = (p.A).dx
Work transfer per unit mass is defined as the flow work.
Therefore, W/mass =
Since, specific volume ( ) is , then,
The work transferred while transferring the mass of fluid is,
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15. 4. shaft work
• It develops power through a rotating shaft against a resisting
torque.
• Work is given through the rotating shaft or work can be
developed through the shaft.
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16. pdV work in various quasi-static processes
1. Constant pressure (p=c) process
• Isobaric process or isopiestic process
• Work done by the system for the process 1-2 is
since, p1 =p2 = p = c
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17. 2. Constant volume (V=c) process
• Isochoric process
• Work done by the system for the process 1-2 is
since, V1 =V2 = V = c
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18. 3. Process in which pV = C
• Work done by the system for the process
can be calculated as
• Therefore, work done by the system for the process 1-2 is
since,
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19. 4. Process in which pV^n = C where n is a constant which is varies
from 0 to ∞.
• Work done by the system for the
process can be calculated as
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20. • Therefore, work done by the system for the process 1-2 is
since,
Here,
Or,
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21. Free expansion with zero work transfer
• Expansion of gas against a vacuum is called free expansion.
• Assuming a system with two compartments in which one is filled
with gas and the other one is vacuumised. These two
compartments are separated by a partition which a thin
membrane. When the partition is removed, gas rushes to fill the
entire volume of the system by expanding to the vacuumised
compartment. Note that the work given for the removal of
partition is negligible, and hence with no work gas is expanded.
This process of expansion of gas without any work transfer across
the system boundary is called free expansion. i.e.,
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22. Contd…
• Now assume that system is only the gas, then after the removal of
partition, gas expands to the vacuum.
• This process is not a quasi-static process since, the path of gas
expansion will not be able to define due to a rapid expansion of gas.
• In this case, to get a quasi-static process, in the vacuum
compartments, place more no.of partitions. By removing each and
every partitions slowly and steadily, gas expands to the vacuum with
no resistance so that we can achieve intermediate equilibrium states
and hence the path can be identified.(Here also work involved to
remove all the partitions is neglected.)
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23. HEAT TRANSFER
• Another form of energy in transit.
• Due to the temperature difference between the system and
surroundings heat energy will be transferred. Its a boundary
phenomenon occurs only across the boundary of the system. i.e.,
• “Heat is a form of energy that is transferred across a boundary by
virtue of temperature difference.”
• Heat transfer (HT) occurs from high temperature system to low
temperature system.
Types of HT
i. Conduction : HT between two bodies in direct contact.
ii. Convection : HT by mass transfer, as transfer of heat between a
wall and fluid system in motion.
iii. Radiation : two bodies are separated by empty space or gases
and heat transfers only through electromagnetic waves.
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24. Contd…
Sign convention
Positive HT: when heat flows into a system (heat addition)
Negative HT: when heat flows out a system (heat rejection)
• The symbol ‘Q’ is used for heat transfer.
• HT is the quantity of heat transferred within a certain time.
• Hence, unit of heat is Joule (J) and heat transfer is J/s or Watt (W)
in S.I. units.
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25. Contd…
• Heat is not that inevitably cause a temperature rise. Similar to
heat transfer, work transfer may also lead to the temperature rise
in a system. Work or heat is not a conserved quantity, and also not
system property.
• In a process in which no heat crosses the boundary of the system
is called an adiabatic process. In an adiabatic process, there is only
work interaction between the s/m and its surroundings.
• A wall which is impermeable to the flow of heat is an adiabatic
wall, whereas a wall which permits the heat flow is diathermic
wall.
• Heat transfer is a path function.
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26. Contd…
• Heat transfer (Q) can be
calculated by using the
similar method we used to
calculate the work transfer.
• So, the HT for the process 1-2
is
• Note that dQ is inexact differential. To get heat transfer quantity,
we need to convert inexact differential to exact differential by
multiplying it is by an integrating factor.
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27. Specific heat and latent heat
Specific heat : amount of heat required to raise a unit mass of the
substance through a unit temperature raise. i.e.,
• sp.heat (c) can be obtained by the process of HT.
If the process is a constant pressure (p = C), then sp.heat is called as
sp.heat at constant pressure, .
If the process is a constant volume(V = C), then sp.heat is called as
sp.heat at constant volume, .
• Heat capacity (C) of the substance = mass of the substance × sp.heat.
• i.e., C = mc
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28. Latent heat : Amount of heat required to change a phase in unit mass of
a substance at constant pressure and constant temperature. i.e.,
Types:
i. Latent heat of fusion(lfu) : amount of heat transferred to melt a solid
to liquid or liquid to solid.
ii. Latent heat of vapourization (lvap) : amount of heat transferred to
convert liquid to vapour or vapour to liquid (latent heat of
condensation).
iii. Latent heat of sublimation (lsub) : heat transferred to convert solid
to vapour or vapour to solid.
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