Carnot cycle.pdf

Carnot Cycle
P
tot
h c
+
q = q + q qh + qc
> 0
V
Heat flows into the
system (q h > 0) to
maintain constant temp
w=−∫PdV The system (the engine) does work.
Δ U = 0 = qtot + wtot
qtot = −wtot
q tot > 0
Heat flows out of the
system (q c < 0) to
maintain constant temp
w tot < 0
qh > qc
Carnot Cycle

w tot
Carnot
Engine
q h
q c
A gas that is undergoing the
four stages of the Carnot cycle
w =− q + q
tot
( )
h c
This will be a neg. number.
Which means the engine did
work (that’s a good thing.)
How much work is done if 50 kJ
of heat flows into the engine and
-40 kJ are returned to the cold
source ?
Carnot Cycle

Engine Efficiency
Define engine efficiency as the ratio of the total work
done divided by the heat input .
ε =
ε
carn. eng.
carn. eng.
=
w
q
tot
h
q + q
q
h c
T
ε carn. eng.
= 1−
T
h
c
h
q q
= −
T T
h c
h c
Carnot Cycle

P
Carnot Refrigerators
A Carnot fridge is a Carnot Engine in reverse.
w=−∫PdV The system (the fridge)
requires work input. (w tot > 0)
-
V
This makes sense, a
refrigerator must remove
heat from an already cold
source and place it in a hot
sink (the room).
Heat (q h ) flows out of the
system (q h < 0) to
maintain constant temp .
Heat (q c ) flows into the
system (q c > 0) to
maintain constant temp .
Carnot Cycle

w tot
The Room
Carnot
Fridge
q h
q c
The Fridge
A gas that is undergoing the four
stages of the Carnot cycle in reverse.
q = −w
tot tot
But now w tot > 0, so…
q < 0
tot
qh + qc
< 0
qh > qc
q h < 0
q c > 0
More heat is dumped into the room
than is removed from the fridge !
Carnot Cycle

Carnot Refrigerator Efficiency
η =
carn. fri.
η =
carn. fri.
η =
carn. fri.
q
w
c
tot
qc
q + q
h c
Tc
T −T
h c
q q
= −
T T
h c
h c
A household refrigerator’s freezer
compartment works at 255 K. Assuming that
the room’s temperature is 294 K, what is the
maximum efficiency ? How much work is
required to remove 65 J of heat from the
freezer ?
Carnot Cycle