Download PHYS1001 PHYSICS 1 REGULAR Module 2 Thermal Physics Chapter

PHYS1001 PHYSICS 1 REGULAR
Module 2 Thermal Physics
Chapter 18
Second Law of Thermodynamics
References: 18.1 to 18.7
Examples: 18.1 to 18.7
Checklist
Second Law of thermodynamics (a statement of what is impossible)
•
Direction of thermodynamics processes: Heat always flows spontaneously
from a hot object to a cooler one.
•
Impossible to convert heat completely into mechanical work. Max efficient of
a real heat energy < 100%. It is impossible for any system to undergo a
process in which it absorbs heat from a reservoir at a single temperature and
converts the heat completely into work, with the system ending in the same
state in which it began.
•
It is impossible to make a refrigerator that transports heat from a colder body
to a hotter body without the addition of work. A minimum energy input is
required to operate a refrigerator. It is impossible for any process to have the
sole result the transfer of heat from a cooler to a hotter body.
•
Irreversible processes (processes that proceed spontaneously in one direction
but not other) – inherent one-way processes in nature - perfume from an open
bottle will spread throughout a room – the perfume molecules will never
spontaneous gather back into the bottle; miscible liquids left to themselves
always tend to mix, not to unmix.
•
No engine can be more efficient than a Carnot engine operating between the
same two temperatures.
•
Perpetual motion machines can not be constructed.
•
For an isolated system, the direction of spontaneous change is from a situation
of lesser probability to a situation of greater probability. For an isolated
system, the direction of spontaneous change is from order to disorder. The
entropy of an isolated system increases or remains the same.
a03/p1/thermal/Th180107.doc 8:25 AM 12/12/02
1
•
Reversible processes (equilibrium processes – quasi-equilibrium processes) –
idealised – system always close to being in thermal equilibrium with itself and
its surroundings.
•
Heat enegine – device that transforms heat partly into work (mechanical
energy) – a working substance undergoes a cyclic process.
All heat engines absorb heat QH from a source at a relatively high
temperature (hot reservoir TH), perform some work and reject some heat at
a lower temperature (cold reservoir TC).
First law for a cyclic process
U2 – U1 = 0 = Q – W ⇒ Q = W
The net heat flowing into the engine in a cyclic process equals the net work
done by the engine.
For one cycle QH > 0 QC < 0
net heat absorbed Q = QH + QC = |QH| - |QC|
(Eq. 18.30
net work done W = Q = QH + QC = |QH| - |QC|
(Eq. 18.2)
Thermal efficiency e = W / QH = 1 + QC / QH = 1 - |QC| / |QH| (Eq. 18.4)
•
Internal combustion engine
Compression ratio r = max vol / min vol
r < 10
Four-stroke cycle
Intake stroke – piston moves down reducing pressure in cylinder
enabling mixture to enter - inlet valve closes
Compression stroke – mixture compressed adiabatically to min volume
as piston moves up.
Power stroke – mixture ignited as spark plug fires and heat gas expands
adiabatically to max volume Vmax = rVmin by hot burnt mixture pushing
piston down and doing work.
Exhaust stroke – combusted products expelled as piston moves up.
a03/p1/thermal/Th180107.doc 8:25 AM 12/12/02
2
•
Otto cycle Idealized model of the thermodynamic processes in a typical car
engine.
For r = 8 and γ = 1.4 (air) ⇒ e = 56% (ideal engine) e ~ 35% (real engine).
Know about pV diagram for the Otto cycle.
Efficiency increases with larger r ⇒ engine operates at higher temperatures
⇒ pre–ignition ⇒ knocking sound and engine can be damaged.
•
Diesel cycle – diesel engines operate at higher temperatures than petrol
engines. During the adiabatic compression high temperatures are reached and
then fuel is injected fast enough to keep the pressure constant. The injected
fuel because of the high temperatures ignites spontaneously without the need
for spark plugs.
Know about pV diagram for the Diesel cycle.
For r ~ 18 and γ = 1.4 (air) ⇒ e ~ 68% (ideal engine).
Diesel engines – heavier and harder to start, and are more efficient than
petrol engines. They need no carburettor or ignition system, but the fuelinjection system requires expensive high-precision machining.
•
Refrigerators – heat engine operating in reverse – it takes heat from a cold
place and gives it off at a warmer place, this requires a net input of work.
|QH| = |QC| + |W|
(Eq. 18.8)
Best refrigerator – one that removes the greatest amount of heat |QC| from
inside the refrigerator for the least expenditure of work |W| ⇒ coefficient
of performance, K (higher K value, better the refrigerator)
K=
QC
W
=
QC
QH − QC
(Eq. 18.9)
Refrigeration cycle – refrigerant fluid (working substance); evaporator,
compressor, condenser, expansion value.
Refrigerator, air conditioner, hear pump.
a03/p1/thermal/Th180107.doc 8:25 AM 12/12/02
3
•
Carnot cycle (maximum efficiency for a heat engine)
For maximum heat engine efficiency – avoid all irreversible processes ⇒
every process that involves heat transfer must be isothermal because heat
transfer through a non-zero temperature difference is an irreversible process
and energy will be lost from and system that can never be recovered ⇒ any
process in which the temperature of the working substance changes must be
adiabatic.
eCarnot = 1 −
TC
TH
=
TH − TC
TH
(Eq. 18.14)
The larger the efficiency, the greater the temperature difference. The
efficiency can never be exactly 1 since TC > 0 K.
All Carnot engines operating between the same temperatures have the same
efficiency, irrespective of the nature of the working substance.
Because each step in the Carnot cycle is reversible, the entire cycle may be
reversed, converting the engine into a refrigerator.
K Carnot =
TC
TH − TC
(Eq. 18.15)
High K value, the better the refrigerator, this is when the temperature
difference is small.
a03/p1/thermal/Th180107.doc 8:25 AM 12/12/02
4
Notes
Any device that transforms heat partly into work or mechanical energy is called a
heat engine. Usually a quantity of matter inside the engine (working substance)
undergoes addition & subtraction of heat, expansion and compression and sometimes
with phase changes.
Internal combustion engine: working substance is air & fuel mixture (in / out)
Steam engine: working substance is water (circulates)
Refrigerator: working substance – freon family eg CCl2F2.
HEAT ENGINE
Cyclic process: W = |QH| - |QC|
Hot reservoir (heat source) TH
QH
Engine – working substance
W
QC
useful mechanical work output
Dissipative losses – friction, turbulence
Cold reservoir (heat sink) TC
a03/p1/thermal/Th180107.doc 8:25 AM 12/12/02
5
OTTO cycle – standard petrol engine
TH (peak) ~ 1800 °C
TC (base) ~ 50 °C
ideal efficiency ~ 55 %
P
r~8
real efficiency ~ 30 %
Otto Cycle
3
isothermals
adiabatic
QH
2
4
Po
1
5
QC
released to
surroundings
V
V2
V1
5 → 1: inlet stroke volume increases as piston moves down creating a partial
vacuum to aid air/fuel entering cylinder via the open inlet valve.
1 → 2: compression stroke inlet valve closes piston moves up compressing
the air/fuel mixture adiabatically.
2 → 3: ignition – spark plug fires igniting mixture - constant volume
combustion.
3 → 4: expansion or power stroke – heated gas expands adiabatically as the
piston is pushed down doing work.
4 → 1 and 1 → 5: Exhaust stroke – outlet valve opens and mixture expelled
at constant volume then piston moves up producing a compression at
constant pressure, Po (atmospheric pressure).
In practice, the same air does not enter the engine again, but since an equivalent amount of
air does enter, we may consider the process as cyclic. The compression rate is r = V1 / V2.
a03/p1/thermal/Th180107.doc 8:25 AM 12/12/02
6
Diesel cycle – more efficient than petrol engines, heavier per unit output, often harder to start.
TH (peak) ~ 1800 °C
TC (base) ~ 50 °C
ideal efficiency ~ 65 %
P
r ~ 18
real efficiency ~ 40 %
Diesel Cycle
QH
isothermals
adiabatic
3
2
4
Po
5
1
QC
released to
surroundings
V
V2
V1
5 → 1: inlet stroke volume increases as piston moves down creating a partial
vacuum to aid air (no fuel) entering cylinder via the open inlet valve.
1 → 2: compression stroke inlet valve closes piston moves up compressing
the air adiabatically. No fuel enters during most of the compression
stroke ⇒ no pre-ignition ⇒ larger compression ratio r ~ 15 to 20.
2 → 3: ignition – injection of fuel directly into cylinder just fast enough to
keep pressure approximately constant. High temperature reached: fuel
ignites spontaneously; no spark plugs or ignition system, no
carburettor, expensive high precision machining for fuel injection.
3 → 4: expansion or power stroke – heated gas expands adiabatically as the
piston is pushed down doing work.
4 → 1 and 1 → 5: Exhaust stroke – outlet valve opens and mixture expelled
at constant volume then piston moves up producing a compression at
constant pressure, Po (atmospheric pressure).
a03/p1/thermal/Th180107.doc 8:25 AM 12/12/02
7
Refrigerators – heat engine operating in reverse – it takes heat from a cold place and
gives it off at a warmer place, this requires a net input of work.
|QH| = |QC| + |W|
(18.8)
Best refrigerator – one that removes the greatest amount of heat |QC| from inside the
refrigerator for the least expenditure of work |W| ⇒ coefficient of performance, K
(higher K value, better the refrigerator)
K=
QC
W
=
QC
(18.9)
QH − QC
K = what we want / what we pay for
K = extraction of max heat from cold reservoir / least amount of work
The Refrigeration Cycle
The compressor A compresses the gas
(eg ammonia). The compressed gas heats
up as it is pressurized (orange). The gas
represents the working substance and the
compressor driven by an electric motor
does work W.
QC
The condenser coils B at the back of the
refrigerator let the hot ammonia gas
dissipate its heat QH. The ammonia gas
condenses into ammonia liquid (dark
blue) at high pressure gas (gas → liquid).
The high-pressure ammonia liquid flows
through the expansion valve The liquid
ammonia immediately boils and
vaporizes (light blue), its temperature
dropping to about –35 °C by the
expansion. This makes the inside of the
refrigerator cold by absorption of heat
QC as liquid → gas.
W
QH
The cold ammonia gas is drawn by the
compressor and the cycle repeats.
a03/p1/thermal/Th180107.doc 8:25 AM 12/12/02
8
Refrigerator
QH
Walls of room
QC
W<0
TC
refrigerator
Inside refrigerator
QC = QH - W
Outside
Air Conditioner
QH
TC
QC
Walls of room
W<0
QH = W + QC
Heat Pump
QC
Walls of room
TC
QH
W<0
Outside
a03/p1/thermal/Th180107.doc 8:25 AM 12/12/02
QH = W + QC
9
Carnot Cycle - Conservation of Energy – Second law of Thermodynamics
•
Second Law of thermodynamics → ideal, reversible heat engines < 100 %
efficient in converting work into work.
•
Carnot's theorem (Sadi Carnot 1796 – 1832): Conversion of thermal energy into
other forms of energy is qualitative different from other kinds of energy
conversion. It is easy to convert mechanical energy into internal energy eg, every
time we use a car's brakes to stop. It is not so easy to convert internal energy into
mechanical energy.
•
Conversion of work into heat is an irreversible process. The purpose of a heat
engine is a partial reversal of this process. For the greatest efficiency, must avoid
all irreversible processes → Carnot Cycle. Heat flow through a finite temperature
difference is an irreversible difference ⇒ Carnot cycle can not have heat transfer
with a temperature difference ⇒ heat transfer must occur during isothermal
processes. When the engine takes heat from the hot reservoir at TH, the working
substance must be at TH, otherwise irreversible heat flow would occur, When the
engine discards heat to the cold reservoir at TC, the engine working substance
must be at TC. During processes when the temperature changes, they must be
adiabatic (Q = 0) ⇒ Carnot cycle: Two isothermal and two adiabatic processes.
•
Carnot showed that no heat engine operated cyclically between two temperature
reservoirs is more efficient than that described by the Carnot cycle.
•
1st Law: For one cycle ∆U = Q – W = 0 ⇒ W = QH – QC
•
Heat transferred in a Carnot engine:
•
Efficiency of a Carnot engine: eCarnot = 1 −
a03/p1/thermal/Th180107.doc 8:25 AM 12/12/02
QC
QH
=
TC
TH
TC
TH
10
P
Carnot Cycle
QH
adiabatic
isothermals
3
Diagram not to
scale, adiabats are
much steeper than
shown
4
W
2
1
QC
released to
surroundings
V
1 → 2: Isothermal compression, heat QC rejected to sink at constant
temperature TC.
QC = - n R TC ln(V2 / V1)
∆U = 0
= n R TC ln(V1 /V2)
∆S = - |QC| / TC
2 → 3: adiabatic compression, the pressure and temperature both increase
without any heat flow taking place.
Q=0
TCV2γ −1 = THV3γ −1
γ −1
 V2 
 
 V3 
=
∆U = -W
∆S = 0
TH
TC
3 → 4: Isothermal expansion, heat QH supplied from source at constant
temperature TH, the pressure decreases.
QH = n R TH ln(V4 / V3)
∆U = 0
∆S = |QH| / TH
4 → 1: Adiabatic expansion, the pressure and temperature both decrease
until they have their same initial values, no heat flow occurs.
Q=0
THV4γ −1 = TCV1γ −1
γ −1
 V1 
 
 V4 
=
∆U = -W
∆S = 0
TH
TC
a03/p1/thermal/Th180107.doc 8:25 AM 12/12/02
11
Efficiency for Carnot Cycle
eCarnot =
eCarnot
W
QH
=
QH − QC
QH
= 1−
QC
QH
V
nRTC ln  1 
 V2 
= 1−
V

nRTH ln  4

 V3 ) 
eCarnot = 1 −
V1 V2
=
V4 V3
⇒
V1 V4
=
V2 V3
TC
TH
Alternative proof
∆Scycle = 0 = - |QC| / TC + |QH| / TH
⇒
QC
QH
=
TC
TH
⇒
eCarnot =
W
QH
=
QH − QC
QH
a03/p1/thermal/Th180107.doc 8:25 AM 12/12/02
= 1−
QC
QH
= 1−
TC
TH
12