Phase diagram of water

Carnot Cycle (Ideal Cycle)
T
Q 12
T 1 2
a
W 41
W 23
Q 34
T b
4 3
S
1) Heat absorption at constant
temperature, T a (boiler) 12
2) Isentropic expansion work
output (turbine) 23
3) Heat rejection at constant
temperature, T b (condenser) 34
4) Isentropic compression
(pump) 41
Energy Conservation (1 st Law of Thermodynamics)
Q 12 + W 23 + Q 34 + W 41 = 0
(Note: Q 12
> 0, W 23
< 0, Q 34
< 0, W 41
> 0)
Cycle efficiency, η c = (Useful work out)/(Heat input at T a )
ie η c = (| W 23 | − W 41 )/ Q 12 | = (T a − T b )/ T a = 1 − T b / T a
(Note: T measured in K (absolute temperature) – formal
definition of absolute temperature scale)
Practical difficulties in using a Carnot Cycle
1) Boiler operates only in wet-steam regime otherwise temperature
would rise when all the water has turned to steam, violating
condition for Carnot Cycle
turbine expands wet steam
water droplets hit turbine blades (damage)
2) Maximum temperature (T a ) is limited to ~650 K
efficiency of cycle is severely constrained
3) Compression of water/steam mixture is thermodynamically
unstable (water droplets)
very large volume compressor (expensive)
Rankine Cycle overcomes all these problems
T
2b
2a
T b
1b 1a
2c
S
Rankine Cycle
Step 1:
a) Condense all the steam to water
in the condenser
b) Pumping water to high pressure requires
small volume machine and little energy
T
T b
T a
S
Step 3:
Expand dry steam through a turbine
to generate shaft power
In practice, water droplets still form in
the low pressure end of the turbine, so
the steam is reheated at various stages
Step 2:
Use 3-stage boiler (~ constant pressure)
a) Economiser – water heated at constant pressure
b) Evaporator – water/steam mixture heated at constant pressure
c) Superheater – dry steam heated at constant pressure
[Note that there is a small drop in pressure through the boiler tube
in order to overcome frictional losses]
T
T a
T b
S
HP
from
IP LP
boiler
reheaters
HP: high pressure turbine
IP: intermediate pressure turbine
LP: low pressure turbine
to condenser