pa2001: time and energy thermodynamics 2 nd law cycles efficiency heat engines and refrigerators...
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PA2001: Time and Energy
Thermodynamics
• 2nd Law• Cycles• Efficiency• Heat engines and refrigerators• Entropy
• Kinetic theory of gasses
• Maxwell’s demon
Tipler Chapters 18,19,20
Thermodynamics 2
Dr Mervyn Roy, S6
PA2001: Time and Energy
Thermodynamics
2nd Law
Some processes are allowed by the first law, but never happen…
GAS VACUUM GAS GAS
We must be missing something!
PA2001: Time and Energy
Thermodynamics
Cyclic process
P
V
W1 W = W1 - |W2 |W2
We can extract useful work from a cycle
Work out Work in Work extracted
PA2001: Time and Energy
Thermodynamics
Efficiency
P
V
Q1
Q2
Q4
Q3
W1
W2
In one complete cycle ΔU = 0
Heat in = work extracted + Heat outQ1+ Q2 = (W1–|W2 |) + |Q3+Q4|
Qin = W + |Qout|
Efficiency = W / Qin
1st LawQ = ΔU + W
PA2001: Time and Energy
Thermodynamics
Heat engine
Qh
|Qc|
W
Cold reservoir (Tc)
Hot reservoir (Th)
Qh = W + |Qc|Efficiency = W / Qh
PA2001: Time and Energy
Thermodynamics
Qh
|Qc|
W
Cold reservoir (Tc)
Hot reservoir (Th)
|Qh|
Qc
W
Cold reservoir (Tc)
Hot reservoir (Th)
Refrigerator
W + Qc = Qh
COP = Qc / WQh = W + |Qc|Efficiency = W / Qh
Heat engine
PA2001: Time and Energy
Thermodynamics
|Qh|
Qc
W=0Qc=|Qh|
Cold reservoir (Tc)
Hot reservoir (Th)
Not allowed!
Perfect refrigerator
It is impossible for a refrigerator working in a cycle to produce no other effect than the transfer of thermal energy from a cold object to a hot object.
2nd Law
PA2001: Time and Energy
Thermodynamics
|Qh|
Qc
Cold reservoir (Tc)
Hot reservoir (Th)
Not allowed!
Qh
W
Cold reservoir (Tc)
Hot reservoir (Th)
Perfect refrigerator
It is impossible for a refrigerator working in a cycle to produce no other effect than the transfer of thermal energy from a cold object to a hot object.
Perfect heat engine
Qc=0, Qh=W
Not allowed!It is impossible for a heat engine working in a cycle to produce no other effect than that of extracting thermal energy from a reservoir and performing an equivalent amount of work.
W=0Qc=|Qh|
2nd Law
PA2001: Time and Energy
Thermodynamics
Entropy
Forbidden by 2nd law.
Processes are irreversible
In any irreversible process the system plus its surroundings move to a less ordered state. ‘Less ordered’ means the ability to do work has been lost.
GAS VAC GAS GAS
Entropy, S, measures disorder. S is a state variable like U, P, V, T etc.
For any process the entropy of the universe never decreases
PA2001: Time and Energy
Thermodynamics
Highest efficiency possible?
Carnot engine: Most efficient engine that can operate between two thermal reservoirs.
P
V
Qin
Qout
adiabatic
adia
batic
isothermal
isothermal
SeaGen: 1.2 MW from tides in and out of Strangford Lough (N.I.) through the Narrows.
The turbine rotor blades can be pitched through 180 degrees allowing them to operate in both flow directions – on ebb and flood tides.
Efficiency = 1 - |Qout|/ Qin
Highest efficiency possible = 1 – TC / Th
e.g. Steam Engine. Efficiency = 1 – 273/373
PA2001: Time and Energy
Thermodynamics
Feel the Entropy!
AreaA
Ideal gas
F
piston
1st Law: W = dU + Q
Ideal gas
Elastic band
PA2001: Time and Energy
Thermodynamics
Kinetic Theory
Have related microscopic motion to macroscopic variables!
Relates temperature to average molecular speed
Equipartition of Energy: energy shared equally (kT/2) between all DOF(explains value of cv in an ideal gas)
From each collision, Force, Pressure,Considering the no. of particles which hit wall in
PA2001: Time and Energy
Thermodynamics
Maxwell-Boltzman distribution
• not all molecules in a gas have the same speed• distribution of speeds, , from statistical mechanics
dv
PA2001: Time and Energy
Thermodynamics
2nd Law
GAS VACUUM GAS GAS
2nd law is valid statisticallyHigh order = low probabilityLow order = high probability
is possible, it is just highly improbable
the larger (more macroscopic) the system, the more improbable.
10 molecules, P=1/1024. 20 molecules, P=1/1048576.
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