Work done on system, W. Work is computed by original definition: the component of force moving through a distance. Examples in internal combustion engine.
Heat absorbed by system, Q. Examples in internal combustion engine.
First Law. Energy of system U -- the sum of work done on system W and heat absorbed by system Q -- is conserved, that is, U = W + Q is conserved.
|Heat QH > 0 added at constant TH. Piston moves out: WH < 0 . (1→2)|
|Expanding gas pushes piston as TH drops to TL. (2→3) [adiabatic process (no heatflow)]|
|QL < 0 extracted at TL. Piston moves in: WL > 0. (3→4)|
|Contracting gas drags piston as TL rises to TH.(4→1) [adiabatic process]|
Work done by system W =WL-WH=QH-QL
Reviewing steps in which we ignore work change during heating and cooling and heat changes during work in or work out. In other words, we assume energy is conserved in actual engine.
The efficiency is the work done (W) compared to the total energy input QH.
|=||(QH- QL)/QH||(Thermo 1st law; conservation of energy|
|=||1 - TL/TH||Q ∝T (coming attraction)|
In examples above, we used "ideal gas" but many engines used different fluids to optimize performance. In our ideal engine we imagined increasing energy at constant high temperature or removing energy at constant low temperature. (Both impossible of course.) The latent heat is central to picking best fluid.
When a material changes phase -- e.g., ice to water or water to steam -- extra energy is required to convert one 1 kg from one phase into another. These are called Latent Heat of Fusion or Latent Heat of Evaporation, respectively.
|Temp C||kJ/kg||Temp C||kJ/kg|
If added 1 kg of ice at 0 C to 10 kg of water at 10 C, what is temperature of final mixture?
Ice will melt and form 11 kg of water. The specific heat of water is
345=(10+1)*(10-T)*4.2 or T = 10 - 345/11./4.2 = 2.5 C.
For water at 20 C (68 F), 3 parts ice, lower temperature to 1 C.
Work, W, is that done to system.
But for efficiency use Wdone by system.
Heat, Q, is heat added to system.
Energy = W + Q is conserved: Thermo. 1st Law
Engine transfers heat energy into work (e.g., internal combustion engines) or work into heat transfer (e.g., refrigerator or heat pump).
Efficiency of heat engine is
Wdone/Qhot, in other words, work done compared
to total heat input.
Conservation of energy, Wdone = Qhot- Qcold, then efficiency = Wdone/Qhot = 1 - Qcold/Qhot < 1.
heat pumps, enthusiastic sales staff typically use
coefficient of performance = (heat out)/(work done),
that is, CP=Qhot/(Qhot- Qcold) > 1.
Kelvin found absolute scale of temperature, Kelvin (K). Nothing can be colder. (0 K = -273 C = -459 F).
Kinetic energy. In an ideal gas,
average energy of any molecule is (3/2) kb
T. Here kb is a (Boltzmann) constant so
kbT in joules.
In an engine driven by an ideal gas, the energy transferred is the difference in the kinetic energy.
Qhot- Qcold ∝ Thot- Tcold.
In any material, over small temperature change (ΔT),
thermal energy change (ΔQ) is
proportional to temperature, connected by
specific heat capacity C: ΔQ = C ΔT.
Typical value of heat capacity. (Water conspiracy)
One calorie heats 1 gram of water 1 degree C.
Heat capacity of water 1 cal/g-C = 4.2 kJ/kg-C is typical of many materials, namely kJ/kg-C.
In closed system, available thermal energy to do work can never be completely used.
Since entropy is thermal energy unavailable to do work; in closed system entropy can never decrease.
For closed universe, its entropy increases (Clausius).
First Law: QH = W + QL.
efficiency = (QH - QL)/QH = 1 - QL/QH.
Thermal energy is proportional to temperature.
efficiency =1 - TL/TH < 1.
Second Law. W < QH - QL.
efficiency < 1 - TL/TH
First law: can't use all heat input for work, only net.
Second law: can't use all the net heat. Really can't win.
The smaller TL/TH the better.
For tri-class seating with 250 seats, 3000 mile flight, the relative fuel consumption per trip has dramatically improved. At the introduction of each: (current four-engine)/(current two engine)/7E7: 2.4/2.0/1.0!
Changes in first-law efficiency. Based on using turbine exit for high temperature and compressor exit for low temperature.
|Year||TL||TH||TH||TH||Wrong ε||Right ε|
Short history of development of thermodynamics.