[精品]Applications of the Second Law-Prof. Zoltan Spakovszky.pdf

Applications of the Second Law
[VN-Chapter 6; VWB&S-, , , , , , ]
Limitations on the Work that Can be Supplied by a Heat Engine
The second law enables us to make powerful and general statements
concerning the maximum work that can be
QH
derived from any heat engine which operates in
a cycle. To illustrate these ideas, we use a TH
Carnot cycle which is shown schematically at
the right. The engine operates between two heat Carnot cycle
reservoirs, exchanging heat
We
QH with the high temperature reservoir at TH
and QL with the reservoir at TL.. The entropy
changes of the two reservoirs are:
∆=<QH TL
SH ; QH 0
TH QL
∆=>QL
SL ; QL 0
TL
The same heat exchanges apply to the system, but with opposite signs; the heat received from the
high temperature source is positive, and conversely. Denoting the heat transferred to the engines
by subscript “e”,
QQQQ=−; =−.
He HLe L
The total entropy change during any operation of the engine is,
∆∆∆∆total =++
SSSS{H {L {e
Reservoir Reservoir Engine
at TH at TL
()∆<
For a cyclic process, the third of these Se is zero, and thus (remembering that QH 0),
∆∆∆total =+=+QH QL
SSSHL ()
TH TL
For the engine we can write the first law as
∆==+−0 (cyclic process) .
UQQWeHe Le e
Or,
WQ=+ Q
eHe Le
−−
= QQHL.
Hence, using ()
 T 
WQTSQ=−−∆ total +  L 
eHL H 
TH
1C-1
 T 
=−()Q 1− L − TS∆ total .
H  L
 TH 
The work of the engine can be expressed in terms of the heat received by the engine as
 T 
WQ= ()1− L − TS∆ total .
eHe  L
 TH 
The upper limit of work that can be done occurs during a reversible cycle, for which the total
entropy change ( ∆Stotal ) is zero. In this situation:
 T 
Maximum work for an engine working between TT and : WQ= ()1− L 
HLeHe 
 TH 
Also, for a reversible cycle of the engine,
Q Q
H +=L 0.
TH TL
These constraints apply to all reversible heat