18 heat and the first law of thermodynamics heat capacity and specific heat change of phase and...
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18 Heat and the First Law of Thermodynamics
• Heat Capacity and Specific Heat
• Change of Phase and Latent Heat
• Joule’s Experiment and the First Law of Thermodynamics
• The Internal Energy of an Ideal Gas
• Work and the PV Diagram for a Gas
• Hk: 31, 37, 47, 51.
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Heat & Internal Energy
• heat is energy that flows due to temperature differences. SI Unit: joule
• internal energy is the total energy of an object in its center of mass reference frame
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Specific Heat Capacity
• The amount of heat needed to raise 1kg by 1°C
• c = Q/mT SI Unit: J/kg·°C
• m = mass receiving (or emitting) heat
• T = temperature change
• Q = mcT
• /
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Example: 300J of heat are added to 100grams of a substance. The temperature rises by 2.20 degrees C.
CkgJCkg
J
Tm
Qc
/1364
)20.2)(1.0(
300
The specific heat of the substance is:
Example: Calorimetry
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Other Heat & Energy Units:
JcallbftBtu 10542527781
Jcal 184.41
CalJkcal 141841
calJatmL 22.243.1011
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Example Conversion
WBtu
J
s
h
h
Btu3500
1054
3500
000,12
A Gas Range is quoted (incorrectly) as “12,000 Btu”. The equivalent power for an Electric Range in watts is:
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Solid/Liquid Transformation
• Melting• Heat in• KE breaks bonds• Molecules move• Liquid forms
• Freezing• Heat out• Molecules lose KE• Settle in one place• Solid forms
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8
Energy in Phase Change
• Energy added:
• solid liquid gas
• energy released:
• gas liquid solid
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Liquid/Gas Transformations
• Evaporation• Highest KE molecules
escape liquid from surface
• Evaporative cooling, e.g. sweat evaporates cooling your body
• Boiling• Highest KE molecules
form gas bubbles throughout
• Hot gas bubbles rise and escape at surface
• Liquid has passed heat out, e.g. simmering at constant temperature
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Latent Heat• Energy needed to melt or vaporize 1kg
of a substance.• Latent Heat, L = Q/m. • Q = mL.• Example: 2.5kg of ice at 0.0°C melts
into 2.5kg of water at 0.0°C.
)/5.333)(5.2( kgkJkgmLQ f
kJ830
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Joule’s Experiment confirmed the mechanical equivalent of heat.
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1st Law Thermodynamics
intbut feature new a isheat
: tocompare
EE
EW
sys
sysext
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18-4 Internal Energy of Ideal Gas
• E-internal is proportional to the absolute temperature
• internal energy is in the kinetic energy of the molecules of the gas
• /
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Work and the PV Diagram
Vf
Viongas PdVW
it.on done be work topositivefor order
in dV) (negative compressed bemust Gas
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Gas Processes
• Isobaric = constant pressure
• Isometric (Isochoric) = constant volume
• Isothermal = constant temperature
• Ex.
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Summary:
• specific heat is material dependent.
• latent heats; objects change phase at constant temperature.
• calorimetry: science of heat measurements
• 1st law of thermo. is energy conservation
• mechanical equivalent of heat
• Pressure x volume = work
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Example: Human vs. Gasoline Engine
Lance Armstrong: 460W V8: 200hp
Power Ratio = 200hp/(460/746)hp = 332 times more
Lance: (460W)(21,600) = 9.9 MJ = 2370 Cal
Energy Consumption (6h = 21,600s):
V8: (332 times more) = 3.3 GJ = 788,000 Cal
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Which of the following is a unit of heat?
1 2 3 4
0% 0%0%0%
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
21 22 23 24 25 26 27 28 29 30
1. N/m
2. N/m2
3. N·s
4. N·m
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Heat is added to a system and the change in internal energy of the system is 1/3 of the heat added. Which of the following is true?
1 2 3
0% 0%0%
1. Work on system is +
2. Work on system is –
3. Work on system is 0
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40
41 42 43 44 45 46 47 48 49 50
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When not colliding, molecules of an ideal gas
1 2 3
0% 0%0%
1. Attract
2. Repel
3. Neither attract or repel
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40
41 42 43 44 45 46 47 48 49 50
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Molecules in an ideal gas
1 2
0%0%
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
21 22 23 24 25 26 27 28 29 30
1. Never collide
2. Sometimes collide
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18-5Work and PV Diagrams
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Work and PV
• [PV] = (N/m2)(m3)= joule = energy
• Work done by an expanding gas:
• Work done by gas during isothermal expansion:
f
i
V
Vby PdVW
i
fisothermalby V
VnRTW ln,
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Internal Energy of an Ideal Gas
• is proportional to temperature of gas
• internal energy is in the kinetic energy of molecules of the gas