The Second Law of Thermodynamics

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27 Οκτ 2013 (πριν από 4 χρόνια και 11 μέρες)

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ME 152

1

The Second Law of
Thermodynamics

Cengel & Boles,
Chapter 5

ME 152

2

The Second Law of
Thermodynamics


So far we have studied:


conservation of energy (i.e., First Law
of Thermodynamics)


conservation of mass


tabulated thermodynamic properties
and equations of state (e.g., ideal gas
law)


There is a need for another law


one
that tells us what sort of processes
are possible while satisfying
conservation principles

ME 152

3

Second Law Statements


Like the 1
st

Law, the 2
nd

Law of
Thermodynamics is based upon a long
history of scientific experimentation


There is no single verbal or math
statement for this Law
-

instead, there
is a collection of statements,
deductions, and corollaries regarding
thermodynamic processes

that
together form the 2
nd

Law


Two popular statements:


Clausius statement


Kelvin
-
Planck statement

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4

Kelvin
-
Planck Statement


“It is impossible for any device
that operates as a cycle to
receive heat from a single
thermal reservoir and produce
an equivalent amount of work”

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5

Clausius Statement


“It is impossible to construct a
device that operates as a cycle
whose sole effect is the transfer
of heat from a lower temper
-
ature reservoir to a higher
temperature reservoir”

ME 152

6

Thermodynamic Cycles


Cycle energy balance






Types of cycles


heat engines, (aka power cycles)


refrigeration and heat pump cycles


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7

Heat Engines


Net (cycle) work output:






Thermal efficiency


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8

Refrigeration & Heat
Pump Cycles


Net work input:





Coefficient of performance (COP)


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9

Reversible Processes


Reversible Process:

a process that
can be reversed, allowing system
and surroundings to be restored to
their initial states


no heat transfer


no net work


e.g., adiabatic compression/expansion
of a gas in a frictionless piston device:

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10

Reversible Processes, cont.


Reversible processes are considered
ideal
processes


no energy is
“wasted”, i.e., all energy can be
recovered or restored


they can produce the maximum amount
of work (e.g., in a turbine)


they can consume the least amount of
work (e.g., in a compressor or pump)


they can produce the maximum KE
increase (e.g., in a nozzle)


when configured as a cycle, they
produce the maximum performance
(i.e., the highest

th

or
COP
)

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11

Irreversible Processes


Irreversible Process

-

process that
does not allow system and surroun
-
dings to be restored to initial state


such a process contains “irreversibilities”


all real processes have irreversibilities


examples:


heat transfer through a temperature difference


unrestrained expansion of a fluid


spontaneous chemical reaction


spontaneous mixing of different fluids


sliding friction or viscous fluid flow


electric current through a resistance


magnetization with hysteresis


inelastic deformation


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12

Internally Reversible
Processes


A process is called
internally
reversible

if no irreversibilities occur
within the boundary of the system


the system can be restored to its initial
state but not the surroundings


comparable to concept of a point mass,
frictionless pulley, rigid beam, etc.


allows one to determine best theoretical
performance of a system, then apply
efficiencies or correction factors to
obtain actual performance


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13

Externally Reversible
Processes


A process is called
externally
reversible

if no irreversibilities occur
outside the boundary of the system


heat transfer between a reservoir and a
system is an externally reversible
process if the outer surface of the
system is at the reservoir temperature

ME 152

14

The Carnot Principles


Several corollaries (the Carnot
principles) can be deduced from the
Kelvin
-
Planck statement:


the thermal efficiency of any heat
engine must be less than 100%





th

of an irreversible heat engine is
always less than that of a reversible
heat engine


all reversible heat engines operating
between the same two thermal
reservoirs must have the same

th


ME 152

15

The Kelvin
Temperature Scale


Consider a reversible heat engine
operating between
T
H

and

T
L

:









Kelvin proposed a simple relation:


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16

The Kelvin Temperature
Scale, cont.


Kelvin’s choice equates the ratio of
heat transfers in a reversible heat
engine to a the ratio of absolute
temperatures


Need a reference to define the
magnitude of a kelvin (1 K)
-

the
triple point of water is assigned
273.16 K:


ME 152

17

Maximum Performance
of Cycles


Carnot Heat Engine:




Carnot Refrigerator:





Carnot Heat Pump:




ME 152

18

The Carnot Cycle


The Carnot cycle is the best
-
known
reversible cycle, consisting of four
reversible processes:


adiabatic compression from
temperature
T
L

to
T
H


isothermal expansion with heat input
Q
H

from reservoir at
T
H


adiabatic expansion from temperature
T
H

to
T
L


isothermal compression with heat
rejection
Q
L

to reservoir at
T
L


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19

The Carnot Cycle, cont.


Note:


the heat transfers (
Q
H
,
Q
L
) can only be
reversible if no temperature difference
exists between the reservoir and system
(working fluid)


the processes described constitute a
power cycle; it produces net work and
operates clockwise on a
P
-
v

diagram


The Carnot heat engine can be reversed
(operating counter
-
clockwise on a
P
-
v

diagram) to become a Carnot
refrigerator or heat pump


the thermal efficiency and coefficients
of performance of Carnot cycles
correspond to maximum performance