A generalized heat engine Could be reversible or irreversible A generalized heat engine Absorbs an amount of heat from a body at temperature for an infinitesimal part of the cycle ID: 505153
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Slide1
p
V
A generalized heat engine
Could be reversible or irreversibleSlide2
A generalized heat engine
Absorbs an amount of heat from a body at temperature
for an infinitesimal part of the cycle.
Slide3
p
V
Isotherm 1
Adiabat
1
Adiabat
2
Isotherm 2
Since the work done on/by the gas along the
adiabats
cancel each other out, bringing them closer to each other reduces the total work done by the Carnot engine.Slide4
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V
Isotherm 1
Adiabat
1
Adiabat
2
Isotherm 2
Since the work done on/by the gas along the
adiabats
cancel each other out, bringing them closer to each other reduces the total work done by the Carnot engine.
Work done
by
the gas is then
Slide5
A generalized heat engine
Set up a Carnot engine which absorbs an amount of heat
, does work
and rejects heat
to the body at temperature
(using (1))
Adjust the Carnot cycle such that
Slide6
For each “narrow” Carnot engine:
Slide7
A generalized heat engine
For the generalized heat engine:
(
for the cycle and
is the work done
by
the engine)
In each infinitesimal segment of the engine cycle it absorbs an amount of heat
from a body at temperature
(
is different for each segment).
Slide8
Work done by all the little Carnot engines
What is the overall effect of all the little Carnot engines and the main generalized engine?
Each Carnot engine absorbs heat
from the reservoir at temperature
and reject an amount of heat
to the body at temperature
. The main engine absorbs all the heat rejected by the little Carnot engines and produces an amount of work
.
Also
Slide9
What is the overall effect of all the little Carnot engines and the main generalized engine?
Each Carnot engine absorbs heat
from the reservoir at temperature
and reject an amount of heat
to the body at temperature
. The main engine absorbs all the heat rejected by the little Carnot engines and produces an amount of work
.
Violates Kelvin-Planck statement of the second law unless the total work done:
Since
i.e.
Claussius
inequalitySlide10
A generalized heat engine
Slide11
A generalized heat engine
The
Claussius
inequality shows that the main engine needs to reject some of the heat it absorbs from the tiny Carnot engines, which means some of the tiny Carnot engines are actually tiny Carnot refrigerators putting some heat back to the reservoir at temperature
.
Slide12
A generalized
reversible
heat engine
Hence, all the heat absorbed from the reservoir at temperature
by the Carnot engines is put back in the reservoir by the Carnot refrigerators.
I
f
the main engine is irreversible, some dissipative work has been done and the total work
whereas, if the main engine is reversible, no dissipative work has been done and
Slide13
Hence:
For a general cycle:
For an irreversible cycle:
For a reversible cycle:
Slide14
Thermodynamics is a funny subject. The first time you go through it, you don't understand it at all. The second time you go through it, you think you understand it, except for one or two small points. The third time you go through it, you know you don't understand it, but by that time you are so used to it, so it doesn't bother you any more.
Arnold
Sommerfeld