Hot Packs and Cold Packs
• Common Medical “Over the Counter” products
– “Universals” use mechanical heat storage
• Put in freezer or microwave, then to injury
• Temporary use, but can be recycled
– “Instant” packs involve chemical reactions
• Exothermic and Endothermic chemistry
• Usually single-use, but no pre-heating or cooling required
• We will explore these chemical types in today’s experiment
1
Thermal Semantics
• Temperature
– A quantitative measure of “hot and cold”
• Arbitrary scales; Fahrenheit, Centigrade, Kelvin
• An indicator of kinetic energy content
– Does not depend on amount of material
• Ocean & tea cup can have same temperature
• Heat
– A quantitative measure of energy transfer
• Measured in Joules or Calories
• Energy flows from hot to cold spontaneously
• Transfer by conduction or radiation
– Depends on amount of material involved
• More material involves more heat transfer
• Ocean has more heat than a tea cup of water
2
Temperatures around the World
left picture refers to January temperatures
Heat energy is delivered by solar radiation
Temperature difference is a result of unequal heat delivery
3
Global Temperature History
Short term “warming”, but long term trend is “cooling”
Global Warming
Current trend began >10k years ago,
are we now “between glacial periods”?
Changes in Energy
• Heat Energy change requires definitions
– Viewpoint is perspective of system changing
• Negative Energy considered as LOSS
– Heat flowing OUT OF a fireplace or oven
– Oven loses heat when oven door opens
• Positive Energy viewed as net GAIN
– Heat flows INTO an ice cube to melt it
– Kitchen warms due to open oven door
– Energy change is algebraic difference
• Definition: E after – E before = ΔE change
• Depends only on the initial and ending conditions
– NOT dependent on the path taken
– Ice sample could be melted 10 times and frozen 9
» Same result as melted once
6
James Joule experiment
demonstrated equivalence of potential energy and heat
7
Energy (Enthalpy) of Thermal Change
• “Enthalpy” or ∆H indicates Thermal energy
• Thermal Changes due to Chemical Reactions
– Exothermic reaction = heat generated
• Enthalpy sign is NEGATIVE (heat flowing away from system)
– Thermite reaction, neutralization
– burning gasoline, fireplace, hot tub
– body heat from food, rubbing hands to keep warm
– Endothermic reaction = heat absorbed
• Enthalpy sign is POSITIVE (heat flows into the system)
– Melting Ice, frozen foods
– Evaporation of water & other liquids absorb heat
– Cold can of soda warming on counter
– Choice of direction was arbitrary (like electron charge)
• Might not be intuitive, but consistent with other definitions
8
Thermodynamics
Losing Energy
• EXOTHERMIC
– Reactions which generate and/or lose heat
– Energy is transferred to surroundings
• Burning leaves, coffee cooling, moving automobile
– ΔH or “Enthalpy” is term for heat transfer
•
•
•
•
-ΔH or “Enthalpy” is negative for Exothermic
(-) Enthalpy becomes part of chemical equation
Enthalpy usually in kJ per Mole
Total energy depends on total quantity
9
EXOthermic reaction (-ΔH)
Producing heat or thermal energy by burning fuel,
converting chemical (or nuclear) into kinetic or heat energy
10
Thermodynamics
Gaining energy
• ENDOTHERMIC
– Reactions which extract and/or gain heat
– Energy is transferred into the object
• Melting ice, coffee being made (water heated)
• +ΔH or “Enthalpy” is term for heat input
– ΔH “Enthalpy” positive (+) for Endothermic
• (+) Enthalpy becomes part of chemical equation
• Enthalpy usually in kJ per Mole
• Total energy depends on total quantity
11
ENDOthermic reaction (+ΔH)
Absorbing heat energy from environment
12
Air Conditioning = ENDOthermic
cooling results from evaporation reaction absorbing heat
accompanied by exothermic condensation at radiator
13
14
Water Energy
Making water from elements releases heat energy
splitting water into elements requires electrical energy
15
Bond Energy
• Heat results from rearranging chemical bonds
– Reducing available energy (reactants-products) releases energy
• Burning wood, animal metabolism
– Increasing chemical energy (products-reactants) absorbs energy
• Photosynthesis, melting ice
• Impractical to measure ΔH for every known reaction
– Billions of chemical combinations
– But use of common bonds provides a practical answer …
• Can use common “features” to divide and conquer
– Bond breaking energy can be determined for reference cases
• Carbon-Carbon bonds (single C-C, double C=C, triple C≡C)
• Diatomic molecules (Cl2, H2, O2, etc.)
– Use known bond energies to estimate new combinations
• Algebraic sum of the bond energy components
• Must use balanced equations and appropriate multipliers
16
Sample Bond Energy Calculation
Burning of Hydrogen in Air, producing heat
Tables of data differ, but have similar values
17
A few common bond energies
18
Table of Bond Energies combustion heat output
19
A home furnace example
We can predict heat from burning methane via bond energies
• Burning Methane CH4+ 2O2  CO2 + 2H2O
• Reactants:
– 4 * C-H bonds x 414kJ/mol * 1mol= 1656kJ
– O=O bond = 498kJ/mol * 2mol = 996
– Total reactants bond energies = 2652kJ
• Products:
– 2 * C=O bonds x 803kJ/mol = 1606kJ
– 2 * H-O bonds x 464kJ/mol * 2 mol = 1856kJ
– Total products bond energies = 3462 kJ
• Change = 2652 - 3462 = - 810 kJ
–
–
–
–
–
Literature value comparison = - 803 to - 889kJ/mole
Negative energy change means Exothermic
Products more tightly bonded than reactants
Takes more energy to pull products apart
Excess energy released as Heat
20
Standard State
• Must define “state” of material for reference
– Gas, Liquids, Solids have different energy content
• Evaporation of water cools (energy loss 44kJ/mole)
• Compression of refrigerant heats it (energy gain)
– “STP” is a definition for reference (standard) state
• Reference temperature (typically 0 or 25 degrees Celsius)
• 1 atmosphere of pressure
• Concentration of 1.00 Moles per Liter (usually)
21
Heats of reactions
your home furnace in chemical terms
one last step involves the water vapor
Two reactions can be combined (both of these exothermic)
Burning of Methane, and condensation of water vapor. A
thermodynamic model of the furnace in your house.
CH4(g) + 2O2(g) CO2(g) + 2 H2O(g) ΔH = - 810kJ/mol
H2O(g)  H2O(aq) a change of state
ΔH = - 44 kJ/mol
• Evaporation absorbs heat, so condensation yields heat
• Stoichiometry requires consistent number of moles
2H2O(g)  2H2O(aq)
ΔH = - 88 kJoule
22
Heats of reactions
Can add the equations, molecules AND reaction energy
• Net reaction, adding the two:
CH4(g) + 2O2(g) CO2(g) + 2 H2O(g) ΔH = -810 kJoule
2H2O(g)
 2H2O(aq)
ΔH = - 88 kJoule
----------------------------------------------------------------------------CH4(g) + 2O2(g) CO2(g) + 2 H2O(aq) ΔH = -898kJoule
• Magnitudes of heat energy combine same as for the
molecules in a chemical reaction
23
Some mechanisims
24
Mechanism for heat of solution
25
Heat of solution (dissolving)
26
Calorimeter in a cup
27
We will use a simple calorimeter
styrofoam cups for insulation
swirling better than stirring
28
What’s wrong with this picture?
(recall James Joule’s experiment)
29
Energy Dimensions
• Original definition is “calorie” (small c)
– Energy to raise temp.1 gram (1 ml) water 1.0oC
– Turned out to be inconveniently small
• Usual quotation in kcal = “Calorie” (big C)
– Energy to raise temp 1.00 liter water by 1.0oC
– Calories are NOT in S.I. (MKS) dimensions
– Commonly used for food products
• SI or ISO unit of energy is “Joule”
– 1 watt for one second = 1 Joule
– Conversion is 4.184 Joule/calorie
– Same thing is 4.184 kJ/kcal = 4.184 kJ/Calorie
30
Our Procedure
• Perform an EXOTHERMIC reaction
– CaCl2 dissolving in water produces heat
– Make a plot to determine maximum temp.
– Use Q=m*ΔT*c = calories
• C is a constant for water = 1.00
– Calculate kcal per mole
• Moles from mass of salt & formula weight
• Compare to literature values, how close?
31
Calculations
• Similar to burning of food experiment
– Heat is delivered to measured mass of water
• Calories into water + salt, Q = m*c*∆T
•
•
•
•
•
Q = heat in calories
M = actual mass of water + salt ( ≈ 120gram)
C = specific heat of water = 1 cal/(gm*∆T)
Q = 120gm*1cal/(gm*∆T)*∆T = calories
If Q positive, solution gets COLD
• If Q negative, solution gets HOT
32
Procedure
• Water
– Weigh empty cup and with ≈100mL water
– Obtain mass of water in grams
• Salt
– Weigh container without & with salt
– Obtain mass of salt in grams
• Temperature
– take initial temperature of water
• Mix salt and water
– Take temp. every 10 seconds for first 3 minutes
– Take temp. every 30 seconds for another 2 minutes
– Swirl water in cup to mix between readings
• Plot the data
33
HEATING REACTION
Temperature Centigrade
Heat from mixing H2O + CaCl 2
60.0
55.0
50.0
45.0
40.0
35.0
30.0
25.0
20.0
15.0
0
100
200
300
400
Time in Seconds
34
Calculation Procedure
• Use graph to determine maximum temperature reached
• Calculate calories produced
– (water grams + salt grams) * ΔT = calories
• Calculate energy per mole derived from salt
– Calories / moles = energy per mole
– Convert to kJ/mole for literature comparison
• Calories / 4.182 = Joules
• Joules / 1000 = kJoules
– Compare to literature values
• - 82.0 kJ/mole for CaCl2 (exothermic) is customary value
• How close did you get ?
• Calculate error = (literature-experimental) / literature
• Answer *100 = percent error
35
Sample Calculation
Min temp
21.00
Max temp
50.00
∆T
29.0
empty
cup
with
content
content
Grams
Water
5
105
91.06
Calcium Chloride
15
35
20.01
Mass of reactants
111.07
Starting Temperature of reactants (from graph data) =
Maximum temperature (from graph data) =
ΔT =
21.0
50.0
29.0
o
o
C
C
Mass of calorimeter contents (grams of water and salt) =
Specific heat of reaction product (given value) =
q = m*∆T*Cp (Cp=specific heat) =
111.070
1.000
3,221
grams
calories/(oC*gram)
calories
Grams of salt changing water temperature =
Formula weight of CaCl2 [40.078+(2*35.45)] =
Moles of CaCl2 =
20.01
110.98
0.1803
from data above
gm/mole
moles
Calories per mole of CaCl2 =
17,864
calories/mole
(17,864)
calories/mole
4.18
Joules/calorie
Reaction was exothermic (got HOT), so ∆H must be negative =
conversion factor for calories to Joules =
heat output in Joules/mole =
(74,673)
Joules/mole
heat output in kJoules/mole =
(74.67)
kJoules/mole
Literature value for CaCl2 dissolving in water =
(82.0)
kJoules/mole
deviation from literature value =
-8.9%
PerCent
36
2nd half of experiment
• Repeat for ENDOTHERMIC reaction
– NH4Cl in water absorbs heat
•
•
•
•
•
Measure masses, initial temperature
Mix and measure temperature changes
Plot data
Calc energy absorbed per mole of salt
Compare to literature value
37
COOLING REACTION
Heat Loss from mixing H2O + NH4Cl
Temperature Centigrade
25.0
20.0
15.0
10.0
5.0
0.0
0
100
200
300
400
Time in Seconds
38
Endothermic data example
Min Temp
Max Temp
∆T
7.90
20.00
empty cup
with
content
content
Grams
Water
5
105
92.40
Ammonium Chloride
15
35
20.02
-12.1
Mass of reactants
112.42
Starting Temperature of reactants (from graph data) =
Minimum temperature (from graph data) =
∆t =
20.0
7.9
-12.1
o
C
C
o
C
o
Mass of calorimeter contents (grams of water and salt) =
Specific heat of reaction product (given value) =
q = m*∆T*Cp (Cp=specific heat) =
112.420
1.000
-1,360
grams
calories/(oC*gram)
calories
Grams of salt changing water temperature =
Formula weight of NH4Cl [14.007+(4*1.008)+35.45]
Moles of CaCl2 =
20.02
53.49
0.3743
from data above
gm/mole
moles
Calories per mole of CaCl2 =
(3,634)
calories/mole
Reaction was exothermic (got COLD), so ∆H must be POSITIVE =
3,634
calories/mole
conversion factor for calories to Joules =
4.18
Joules/calorie
heat output in Joules/mole =
15,192
Joules/mole
heat output in kJoules/mole =
15.19
kJoules/mole
Literature value for CaCl2 dissolving in water =
14.7
kJoules/mole
3.3%
PerCent
deviation from literature value =
39
Now you try it
• Report due next week
40
Los Alamos National Laboratory's Periodic Table
Group**
Period
1
IA
1A
2
3
1.008
3
4
H
Li
Be
6.941
9.012
11
12
Na Mg
22.99
4
5
8
9
10
3
4
5
6
7
11 12
------- VIII IIIB IVB VB VIB VIIB
IB IIB
-----3B
4B 5B 6B
7B
1B 2B
------- 8 ------
20
21
Ca
Sc
39.10
40.08
37
38
Rb
Sr
85.47
87.62
Cs
87
Fr
(223)
56
88
6
7
8
9
B
C
N
O
F
22
23
24
25
26
27
28
29
30
13
14
Al Si
32
Y
40
41
42
44
45
46
47
48
49
50
72
73
74
(98)
75
17
18
Cl
Ar
33
34
35
51
52
53
I
101.1 102.9 106.4 107.9 112.4 114.8 118.7 121.8 127.6 126.9
76
77
78
79
80
81
82
83
84
85
Pt Au Hg Tl Pb Bi Po At
138.9 178.5 180.9 183.9 186.2 190.2 190.2 195.1 197.0 200.5 204.4 207.2 209.0 (210) (210)
107
108
109
86
Rn
(222)
116
118
---
()
()
()
59
60
61
62
63
64
111
Xe
131.3
---
(257) (260) (263) (262) (265) (266)
110
54
114
58
106
83.80
---
Lanthanide
Series*
105
36
Kr
112
(227)
104
39.95
Ra Ac~ Rf Db Sg Bh Hs Mt --- --- --(226)
89
Ne
20.18
S
Zr Nb Mo Tc Ru Rh Pd Ag Cd In Sn Sb Te
88.91 91.22 92.91 95.94
57
43
10
16
44.96 47.88 50.94 52.00 54.94 55.85 58.47 58.69 63.55 65.39 69.72 72.59 74.92 78.96 79.90
39
4.003
15
26.98 28.09 30.97 32.07 35.45
31
2
He
P
Ti V Cr Mn Fe Co Ni Cu Zn Ga Ge As Se Br
Ba La* Hf Ta W Re Os Ir
137.3
5
10.81 12.01 14.01 16.00 19.00
19
132.9
7
24.31
13
14
15 16
17
IIIA IVA VA VIA VIIA
3A 4A 5A 6A 7A
K
55
6
8A
2
IIA
2A
1
1
18
VIIIA
()
()
()
65
66
67
68
69
70
71
Ce Pr Nd Pm Sm Eu Gd Tb Dy Ho Er Tm Yb Lu
140.1 140.9 144.2 (147) 150.4 152.0 157.3 158.9 162.5 164.9 167.3 168.9 173.0 175.0
41
Ice melting
classic example of entropy increase described in 1862 by Rudolf Clausius
as an increase in the disagregation of the molecules of the body of ice.
42
Calories in the food
• Calories delivered into water, Q = m*c*∆T
•
•
•
•
Q = heat in calories
M = actual mass of water heated ( ≈ 100gram)
C = specific heat of water = 1 cal/(gm-∆T)
Q = 100gm*1cal/(gm*∆T)*∆T = calories
• Calories into water came from food
– Calories transferred / mass of food = cal/gram
• If 0.5 gram food (preburn-postburn) yields 2 kcal
• 2 kcal / 0.5 gram = 4 kcal/gram for the food
• 1.0 pound (454 gm) of this food yields ≈ 1800 kcal
43
Carbon Fuels
Heat output of fuel results from breaking bonds, releasing energy
• “Heat of Combustion” for carbon fuels (e.g. gasoline, jet fuel)
– Called ΔH of combustion, or Combustion Enthalpy
• Source material always contains C and H
– Numbers of C & H varies tremendously
– Natural products full of variants: linear + branched + ring structures
• Combustion products always contain H2O and CO2
– Sometimes also CO and NOX (N2O, NO, NO2, NO3)
– Depends on amount of oxygen available and temperature
• Theoretically possible to calculate heat of combustion for any fuel
– Works for simple materials (hydrogen, methane, benzene)
– See table for typical values
– Not too practical for “real world” bulk materials
• Too many variations and uncertainties with natural products
• Dissolved dinosaurs and vegetation don’t yield pure chemical products
44
Carbon Fuels
• Fuels have 3 entangled physical properties
– Density (grams per cm^3)
– Molecular Weight (grams per mole)
– Combustion Energy (bond breaking)
• Application defines which is “best”
– Higher density (liquid) fuels good for Automobiles
• 5 to 11 carbons in gasoline (depends on season)
• More moles per gas tank, drive farther between fillings
• Diesel fuel more energy than Gasoline, 11-14 carbons
– Low density (gas) fuels good for domestic use
• Vapor state fuels (methane, propane) easy to handle
• Constant pressure, simple distribution using pipes
• Weight and size of delivery system not important
45
Common Fuels
• Burning Hydrogen (proposed by CA)
– 1 H-H bond = 436kJ/mol (22.4 Liters or 5.9 gal )
– or 436kJ/gram of H2
• Burning Methane (natural gas)
– 4 C-H bond = 1,656kJ/mol, (22.4Liters or 5.9 gal)
– or 1656kJ/mol / 16gm/mol = 106kJ/gm CH4
• Burning Gasoline (octane=C8H18)
– 18C-H & 7C-C bond = 7848+2429 =10,277 kJ/mol
– Or 10,277kJ/mjol/114g/mol= 90kJ/gram of octane
– density = 0.72 gm/mL, 114g/0.72g/mL= 0.16 Liter
46
ISO Energy Definition
• Units of Energy, definition of Joule
• Auto data
– SUV is 4000 lb= 1842kg
– Speed of 62mi/hr = 100km/hr= 27.7 m/sec
– kg*(m/s)^2= 1842*27.7*27.7 = 1.41E6 W-S
47
• Gasoline efficiency
– 18miles/gallon (my Ford Explorer)
– 18mi/g/3.84L/g*1.6km/mile  7.4 km/Liter
– At 700 gr/Liter, gasoline  10.6 meter/gm
– Gasoline energy = 43.6 kJ/gram
– Energy expended = 43.6/10.6 = 4.11 kJ/meter
48
49
50
51
52
Energy Unit Conversions
– ISO Definition: 1 Joule ≡ 1 Watt-Second
– Units conversion yields 4.184 Joule/calorie
– 100 watt device running 1 hour = 36,000 J = 360 kJ
• 100 watts*1 hour*3600 sec/hour = 3.6*10^5 W-s (or Joules)
– 360 kJ / 4.18 kJ/kCal = 86 kcal = 86 Cal
– One 12 oz can (355ml) Coke Classic = 146 kcal = 146 Cal
– 1.7 hour of light bulb use ~ energy in 1 can “Coke Classic”
• Toshiba “Satellite” Laptop, 15V @5A = 75 watts
– 75 is 75% of above light bulb example = 2.7*10^5 W-s
– 270kJ / 4.18 kJ/kcal = 65 kcal
– 2.3 hours laptop energy ~ 1 can of Coke Classic.
– Watt-seconds becoming a commonplace U/M
• Direct links between electricity & chemistry U/M
• Usual specification units for camera flash
– 50 w-s flash lasts 1/1000 sec, intensity = 50,000 watts !
53
Human Energy
• At 2000 kCal / day
– 2.00E6 cal/day * 4.184 j/cal = 8.369E6 J/day
• same as 8.369E6 watt-seconds/day
• 60sec/min*60min/hr*24hr/day=8.64E4 sec/day
• (8.369E6 w-s/day) /(8.64E4 sec/day) = 96.8 watts
– Human energy output ≈ 100 watt light bulb!
• 20 watts to keep brain going
• 80 watts to keep warm, locomotion, organ function
• Issues for A/C and critical environments
• 500 people generate 50kW of heat!
• Clean rooms adjust A/C to match number of people
• Sleeping together keeps us warm (Penguin movie)
54
END of Mini-Lecture
• Now to the experiment
55
Carbon Fuels
Heat output of fuel results from breaking bonds, releasing energy
• “Heat of Combustion” for carbon fuels (e.g. gasoline, jet fuel)
– Called ΔH of combustion, or Combustion Enthalpy
• Source material always contains C and H
– Numbers of C & H varies tremendously
– Natural products full of variants: linear + branched + ring structures
• Combustion products always contain H2O and CO2
– Sometimes also CO and NOX (N2O, NO, NO2, NO3)
– Depends on amount of oxygen available and temperature
• Theoretically possible to calculate heat of combustion for any fuel
– Works for simple materials (hydrogen, methane, benzene)
– See table for typical values
– Not too practical for “real world” bulk materials
• Too many variations and uncertainties with natural products
• Dissolved dinosaurs and vegetation don’t yield pure chemical products
56
Carbon Fuels
• Fuels have 3 entangled physical properties
– Density (grams per cm^3)
– Molecular Weight (grams per mole)
– Combustion Energy (bond breaking)
• Application defines which is “best”
– Higher density (liquid) fuels good for Automobiles
• 5 to 11 carbons in gasoline (depends on season)
• More moles per gas tank, drive farther between fillings
• Diesel fuel more energy than Gasoline, 11-14 carbons
– Low density (gas) fuels good for domestic use
• Vapor state fuels (methane, propane) easy to handle
• Constant pressure, simple distribution using pipes
• Weight and size of delivery system not important
57
Common Fuels
• Burning Hydrogen (proposed by CA)
– 1 H-H bond = 436kJ/mol (22.4 Liters or 5.9 gal )
– or 436kJ/gram of H2
• Burning Methane (natural gas)
– 4 C-H bond = 1,656kJ/mol, (22.4Liters or 5.9 gal)
– or 1656kJ/mol / 16gm/mol = 106kJ/gm CH4
• Burning Gasoline (octane=C8H18)
– 18C-H & 7C-C bond = 7848+2429 =10,277 kJ/mol
– Or 10,277kJ/mjol/114g/mol= 90kJ/gram of octane
– density = 0.72 gm/mL, 114g/0.72g/mL= 0.16 Liter
58
ISO Energy Definition
• Units of Energy, definition of Joule
• Auto data
– SUV is 4000 lb= 1842kg
– Speed of 62mi/hr = 100km/hr= 27.7 m/sec
– kg*(m/s)^2= 1842*27.7*27.7 = 1.41E6 W-S
59
• Gasoline efficiency
– 18miles/gallon (my Ford Explorer)
– 18mi/g/3.84L/g*1.6km/mile  7.4 km/Liter
– At 700 gr/Liter, gasoline  10.6 meter/gm
– Gasoline energy = 43.6 kJ/gram
– Energy expended = 43.6/10.6 = 4.11 kJ/meter
60
61
62
63
64
Energy Unit Conversions
– ISO Definition: 1 Joule ≡ 1 Watt-Second
– Units conversion yields 4.184 Joule/calorie
– 100 watt device running 1 hour = 36,000 J = 360 kJ
• 100 watts*1 hour*3600 sec/hour = 3.6*10^5 W-s (or Joules)
– 360 kJ / 4.18 kJ/kCal = 86 kcal = 86 Cal
– One 12 oz can (355ml) Coke Classic = 146 kcal = 146 Cal
– 1.7 hour of light bulb use ~ energy in 1 can “Coke Classic”
• Toshiba “Satellite” Laptop, 15V @5A = 75 watts
– 75 is 75% of above light bulb example = 2.7*10^5 W-s
– 270kJ / 4.18 kJ/kcal = 65 kcal
– 2.3 hours laptop energy ~ 1 can of Coke Classic.
– Watt-seconds becoming a commonplace U/M
• Direct links between electricity & chemistry U/M
• Usual specification units for camera flash
– 50 w-s flash lasts 1/1000 sec, intensity = 50,000 watts !
65
Human Energy
• At 2000 kCal / day
– 2.00E6 cal/day * 4.184 j/cal = 8.369E6 J/day
• same as 8.369E6 watt-seconds/day
• 60sec/min*60min/hr*24hr/day=8.64E4 sec/day
• (8.369E6 w-s/day) /(8.64E4 sec/day) = 96.8 watts
– Human energy output ≈ 100 watt light bulb!
• 20 watts to keep brain going
• 80 watts to keep warm, locomotion, organ function
• Issues for A/C and critical environments
• 500 people generate 50kW of heat!
• Clean rooms adjust A/C to match number of people
• Sleeping together keeps us warm (Penguin movie)
66