lecture 3-4: exergy, heating and cooling, solar thermal
TRANSCRIPT
Exergy
The following systems all “store” about 1 kW hr of energy
• 36,000 C of charge at a potential of 100 V
• 3600 kg of water at a height of 100 m
• 1/7 litre of petrol
• 3000 m3 of air at 1°C above room temperature
Which of these would you pay the most money for?
Energy is conserved!
So, why do we have an “energy crisis”?
When we “use” energy, we convert it from a more useful form to a less useful form
How to quantify?
Exergy p, V, S, T
p0, T0
A = U + p0 V – T0 S
Often defined relative to “dead state”, where system is in equilibrium with surroundings
A = (U - U0) + p0 (V - V0) – T0 (S – S0)
Can also include (macroscopic) kinetic and potential energy terms
Where chemical species can be exchanged with environment, add chemical potential terms, µ0N
Thermodynamics: An Engineering Approach; Y. A. Cengel, M. A. Boles Fundamental of Engineering Thermodynamics; M. J. Moran, H. N. Shapiro
(also known as “availability”)
Example
dS = dQ/T = c dT/T S = c ln(T/T0)
Heat engines
W
TH
TL
QH
QL
Coefficient of performance, η = W/QH
p, V
TH
TL
QH
QL
Carnot cycle
1-2 Isothermal expansion 2-3 Adiabatic expansion 3-4 Isothermal compression 4-1 Adiabatic compression
Maximum efficiency (reversible)
H
Lrev T
T−= 1η
Heat pump
Refrigerator
W
TH
TL
QH
QL
Coefficient of performance, η = QH/W
LH
Hrev TT
T−
=η
W
TH
TL
QH
QL
Coefficient of performance, η = QL/W
LH
Lrev TT
T−
=η
Exergy
Proof:
dU = δQ + δW = δQ – p dV = δQ – (p – p0) dV – p0 dV = δQ – δWuseful,done – p0 dV
System with U, S, p, T Surroundings at p0, T0
Remove heat –δQ, and increase volume by dV
δWuseful,done = - dU – p0 dV + δQ
−δQ used to run heat engine operating between T and T0, doing work δWHE
δWHE = - (1 - T0/T) δQ = - δQ + T0/T δQ = - δQ + T0 dS For reversible change
(maximum work) Total useful work done, δWu = δWuseful,done + δWHE = - dU – p0 dV + δQ – δQ + T0 dS = - dU – p0 dV + T0 dS
Available work = = (U – U0) + p0 (V – V0) - T0 (S – S0) = exergy ∫dead
initial
udW
Exergetic efficiency
“Second law efficiency”
revex CoP
CoP=η = 1 for ideal, reversible system
E.g. for engine
usedexergydonework
ex =η
coefficient of performance
Is setting fire to fuel to make heat a good thing?
Efficiency for heating
• Reduce temperature difference • Turn the thermostat down
• Reduce heat loss • Increase CoP of heat creation
Leakiness 8 kWhr / day / °C
Heat loss = leakiness × Average temperature difference
kWhr/day
kWhr / day / °C °C
Power required = heat loss / CoP
Reduce leakiness
New leakiness 6 kWh / day / °C
Old leakiness 8 kWh / day / °C
Increase coefficient of performance - use heat pumps
http://www.ecosystem-japan.com/
EcoCute water heater CoP = 4.9
Heating without fossil fuels
Heat pumps, powered by electricity
Ground-source heat pumps
Air-source heat pumps
4 times more efficient than ordinary electric heating
Ideal heat pump performance
Combined heat and power?
“Microgeneration”, “Decentralisation”
(combined heat and power) (cogeneration) Carbon Trust on Micro-CHP
"Micro-CHP is an emerging set of technologies with the potential to provide carbon savings in both commercial and domestic environments."
Efficiency of CHP
EcoCute water heater - CoP = 4.9
Can we do better than CHP? - Heat pumps
Engines
From Cengel & Boles, Thermodynamics
Engine efficiency
Air standard Otto cycle
Carnot efficiency
E.g. r = 8, 800 kJ/kg heat supplied, T1 = 290 K, k = 1.4
T3 = 1575 K, T4 = 701 K, T2 = 666 K
Actual efficiencies only ~20%
123
14 111 −−=−−
−= kth rTTTTη
r = compression ratio = V3/V4 = V2/V1
k = cp/cv
%8213
1 =−=TT
revη
%56=thη
(If heat supplied at T3 and extracted at T1)
From Cengel & Boles, Thermodynamics
Can Carnot efficiencies be achieved?
Stirling engine
1-2 Isothermal expansion 2-3 Cool at constant volume 3-4 Isothermal compression 4-1 Heat at constant volume
Transfer heat to “regenerator”
Recover heat from “regenerator”
Regenerator must be at same temperature as gas ⇒ Reversible
From Cengel & Boles, Thermodynamics
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Ideal Stirling Cycle
Hot gas expands Work out Heat in Transfer gas to
cold cylinder Heat transferred to regenerator
Cold gas contracts Work in Heat out
Transfer gas to hot cylinder Heat transferred from regenerator
From Cengel & Boles, Thermodynamics
More complex than the ideal cycle!
Alpha Stirling Engine
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Beta Stirling Engine
• Single piston for compression/expansion
• Move (insulated, loose fitting) displacer piston to “move” gas from hot to cold region and vice versa
Practical points
• Real efficiencies ≤ 50% • External combustion less easy to regulate • More expensive than diesel engines
The Sun
Roughly a black body
• Temperature ~5800K • Distance 1.5×1011 m • Diameter 1.4×109 m
Stefan’s law
4TbodyblackbyemittedareaunitperPower σ=
42832
45
KmW1075152 −−−×== .
hckπσ
( )1
5
2
12−
−
=
kThchcTB
λλλ exp
Making things hot
Total power radiated by sun 24 4 sunrT πσ
Intensity (W m-2) at distance s 2
24
srT sun
sunσ
Power absorbed by object, radius r 22
24 r
srT sun
sun πσ
In equilibrium, power absorbed = power radiated 242
2
24 4 rTr
srT objectsun
sun πσπσ =
24
41
=
s
rT
T sun
sun
object
For sun, at earth, data from previous slide give ~1400 W m-2
Actual average value at noon, at equator, beyond atmosphere = 1366 W m-2
s radius rsun
radius r
Tobject = 280 K for searth-sun 256 K if 30% reflecting
Making things hotter
• Heat engines run better from high-temperature sources
• But, at high temperatures • Re-radiation increases • Things melt
Solar concentrator
• To increase temperature • Use a greenhouse • Increase the range of angles from which radiation is incident
See website for derivation of optimum temperature
Stirling Energy Systems 14 W/m2
Andasol, Spain
10 W/m2
Photo: ABB
Photo: IEA SolarPACES
Cover every south-facing roof
110 W/m2
10 m2 per person Assume 50% efficient
Solar Thermal
13 kWh per day per person
Real data
3 m2
3.8 kWh/d average
13 kWh/d for 10 m2