Thermodynamics basics

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Thermodynamics basics
Zeroth Law
C
A
B
If A and B and B and C are in thermal equil, then
A and C are in thermal equil. ie. At same T
R Johnson/UAF/CEM/ME 2005
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KE and PE
KE 1/2mv2 PE mgh
So, m 1 kg, v 100 m/s, h 100 m, ?
KE 0.5104 kgm2/s2 5000 J via J
N-m and N kg m /s2

PE 19.8100 kg m2 /s2 980 J
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Thermal, chemical, nuclear energy
1 kg water with ?T 100 C changes internal
energy by ??U 420 kJ via mc ?T with c
4.2 kJ/kg/K
If evap at P 1 atm, ??U 2 MJ
1 kg liquid or gaseous fossil fuel has htg vl
44MJ
E m c2 ?? 9 x 1016 J via c 3 x 108 m
/s
RJ 4.02
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Energy amounts
BMR 70 W 240 Btu/hr
Home htg in Fbks 30 K Btu/hr in winter
Home electrical use 1000 kWh/mo 3.4 MBtu or
rate of 1.4 kW or 5 K Btu/hr
US energy use 90 Q/yr with Q 1015 Btu
? 10 kW/cap
RJ 4.02
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Relative masses
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Properties
h const
C P
SH
T
liq
saturated
P const.

s or v
Water Crit Pt at P 22 MPa, T 374 oC
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SH steam


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Sat. steam
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Properties of Saturated Water
T P vg uf ufg hf
hfg s sfg
oC MPa m3/kg
kJ/kg kJ/kg/K
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vg vs. P
P 0.02 0.05 0.10 vg 7.65 3.24 1.694
P 1 2 4 6 vg 0.194 0.0996 0.0498
0.0324
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hg vs P
P 0.02 0.05 0.1 0.2 0.5 1 hg 2610
2646 2676 2707 2749 2778
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First
First Law
Conservation of Energy
?E Q - W
Q
for system
W
E
eg. Q 100 kJ W 60 kJ
?E 40 kJ
mi
me
Each term gt 0 if by system
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For a cycle
?E 0 so Qnet W which leads to W QH - QL
2nd Law says all of QH cant be converted into
W or ? lt 100
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Closed transient
T
Q - W mu2 -u1
v
eg. Let SH steam at P1 5 MPa and 900 oC cool
at const v 0.1076 m3 /kg to 450 oC STs ? u1
3841 kJ/kg STs ? P2 3 MPa and u2 3020
kJ/kg So Q/ m - 821 kJ/kg
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Heat Xfer
Qdot -k dT/dx k lt 0.1 W/m/K for good
insulators
qdot
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Required insulation thickness
keep resting adult warm at T -10 oC.   ka
0.026 W/m oK and Edot - Qdot   Edot 70
W kA ?T/?x with ?T 40 oC.   70 W 1.04
A/?x W with A (m2 ) ?x (m )   A 2 m2
? ?x 2/70 m 3 cm
30 oC
Ta - 10 oC
2m
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1st Law for CV
dEcv/dt mdot hin - hex Qdot - Wdot
Ecv mcv u 0.5v2 gzcv
We could also put KE PE terms on RHS of 1st eqn.
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Open sys in SSSF ? Qcv mi hi me he Wcv
Q
Qcv - 200 kW
W
i
mi me 3 kg/s
e
hi 3000 kJ/kg he 2600 kJ/kg
Wcv 33000 2600 200 1000 kW
Note dot omitted over Q, W, m
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Throttling
hi he
i
e
X
Eg. Steam at 4 MPa and 700 C exits valve at 0.5
MPa
h 3906 kJ/kg so Te 691 oC via
T 600 (3906 3702)/(3926 3702)
100 With 0.91
T
P
s ? from 7.62 to 8.47 because of
irreversibilities
s
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Steam Properties
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Boiler
e
i
T
Now take sat liq at 4 MPa entering boiler and
heat to 800 C
s
hi hf 1087 and he 4142 kJ/kg So q
he - hi 3055 kJ/kg
Note Tsat 250 C
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Heating of Liquid
Q m cp T2 - T1
Above true whether P const or not as heating
occurs
For water, cp c 1 Btu/lbm/ oF 4.2
kJ/kg/ K
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US Solar Insolation
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Solar water heater
http//www.eren.doe.gov/erec/factsheets/solrwatr.p
df
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NREL photo
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Solar Hot Water
Vancouver Int. Airport
375 K cost and annual savings of 67 K 100
panels heat 800 gph
http//www.solaraccess.com/news/story?storyid5271
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Solar water heating
solarwaterFbks.m NREL Fbks data vls are
monthly averages kWh/m2/day for March - Nov.
for surface tilted at lat angle of 64 deg mo
210 effic1 0.5 0.6 0.7ones(1,4) 0.6 0.5
0.4 Sinsoltilt9 2.4, 4.7, 5.6, 5.3, 5.2,
4.9, 4.2, 3.4, 2.0 avg 3.3 for yr if
mult by 3600, we convert to kJ/m2/day Tl 10
Th 40 rhow 1 kg/liter Cpw 4.2 effic
0.7 Toi Th Tl kJ/kg/K Volw
effic3600.Sinsoltilt9/Cpw/rhow/(Th - Tl) Volw1
3600.effic1.Sinsoltilt9/Cpw/rhow/(Th -
Tl) figure(2) plot(mo,Volw,mo,Volw1,'linewidth'
,2) grid on title('Warm water
prepared','fontsize',16) etc
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Fbks NREL solar data
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Solar Air Heater 1
PV panel
Solar air heater at UAF
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Data from Fieldpoint
1/12/03
UAF Energy Center
http//pug.engr.uaf.edu/data_html\011203_ecenter.h
tml
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Solar Air Heater
8 hr period represented
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Solar Air Heater
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Heat Engines
Receive heat at high T and reject to low T
QL

QH
W
? W/ QH 30
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Carnot Cycle
0
TH
QH
2
3
QL TL s4 s1
QH /TH QL /TL
T
QH TH s3 s2
4
1
QL
TL
W QH - QL
s
? QH - QL /QH
? 1 - TL /TH
Is upper bound for heat engine
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Applications
Diesel electric generators, gas turbines
power plants

http//www.gensetcentral.com/pdf/js170uc.pdf
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Example - DEG
Wel
6 gph fuel

138 K Btu/gal
QL
QH 818 K Btu/hr 242 kW and ? 33
? Wel 81 kW with rest of output as heat
flux up exhaust and rejected to jacket water and
ambient

13.5 kWh/gal
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Second Law
Processes only proceed in certain drcts
Clausius Can't build cyclic device whose sole
effect is heat xfer from cold to hotter body.
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Entropy
or
Heat xfer thru finite ?T is irreversible
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Clausius Inequality
lt 0
Consider Rankine Cycle
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P2 P3 1 MPa T2 100 C T3 350 C
SH vap
T
B
4
x 1
2
1
C
Sat liq
P
P1 P4 100 kPa and sat so T 100 C
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T
3
350 C
boiler
2a
180 C
turb
2
4
100 C
1
cond
s3 7.30
s
1.30
7.36
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Now calc
q23 /T23 q41 / T34
q23 h3 - h2 3051 417 2634 kJ/kg
q41 h1 - h4 - 2258 kJ/kg
q41 / T34 - 2258/373 -6.05 kJ/kg/K
Adiabatic from 1..2 and 3..4
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To calc.
Split into three parts
In CL regime,
h2a h2 /Tavg 762 418/413 0.83
In sat regime,
hfg /Tsat 2015/453 4.45

• h3 - hg /Tavg 3051 - 2778/538
• 0.51 so

In SH regime,

5.79
5.79 - 6.05 - 0.26
Note wnet q23 - q14 515 kJ/kg
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SSSF
Open sys in SSSF ? Sgen m se - si
Q/T
I To Sg Wrev W I
Q
e
i
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Example - ST
8 kg/s at 3 MPa
Q - 300 kW
450 oC
W

hi 3344 he 2769 W 8hi - he - 300
4. 3 MW
0.2 MPa 150 oC
Ex 7-15 CB
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Ex. cont.
si 7.083 se 7.280 kJ/kg/K so Sg
8se - si 300/298 2.56 kW/oK I To
Sg 765 kW Wrev W I 5.07 MW ?2
W/Wrev 85

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If 1 kg water heated isothermally and reversibly
at 100 oC from sat liquid to sat vapor, 1st
Law? Q mu2 u1 Pv2 - v1 mh2
h1 1h2 - h1 1hfg 2257 kJ ?S
Q/T 2257/373 6.048 kJ/K m sfg
T
2
1
s or v
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Environmental Impacts
gt 1272 grams of fossil fuel and chemicals used to
produce a 32-bit DRAM memory chip mass of 2
grams Another 400 grams of fossil fuel
required to produce electricity to operate it
over its lifetime. This doesnt even account for
ultimate disposal cf ratio of 21 for automobile
Environmental Science Technology / January 1,
2003
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