Power Plant Engineering

2.18.2 IDEAL AND ACTUAL EFFICIENCY
A thermionic generator is like a cyclic heat engine and its maximum efficiency is limited by
Carnot’s law. It is a low-voltage, high current device where current densities of 20–50 A/cm
2
have been
achieved at voltage from 1 to 2V. Thermal efficiencies of 10–20% have been realized. Higher values
are possible in future.
Development of thermionic generators is in progress. Practical working prototypes have been
built and feasibility has been proved (1980s). With anode of low work function material (barium oxide,
stron-tium oxide) and cathode of high work-function material (tungsten impregnated barium com-
pound), and temperatures at cathode around 2000°C, power output density of about 6 W/m can be
achieved. Efficiency is about 35%.
The positively charged cathode tends to pull the emitted electrons back. The electrons already in
the gas exert a retarding force on the electrons trying to cross the gap. This pro-duces a space charge
barrier Fig. 2.26 shows the characteristic curve of a thermionic generator with an interspace retarding
potential equivalent to S volts above the anode work function 
Φ
a
.
Potential barrier,
V
c
> 
Φ
c
and V
c 
> 
Φ
a
The current densities are :
J
c
= A
1
T
c
2
c
c
V
kT
e


−




[A/cm
2
]
J
a
= A
1
T
c
2
2
c
V
kT
e


−




[A/cm
2
]
The output voltage across the electrical resistance R,
V
o
= V
c
– V
a
= 
φ
c
– 
φ
a
= 
1
e
(
ε
fa
– 
ε
fc
)
Each electron has to overcome the interspace potential (V
c
– 
Φ
c
) and work function 
Φ
c
when it
leaves the cathode. The net energy carried,
Q
1c
= J
c
(V
c
– 
φ
c
+ 
φ
c
) = J
c
 V
c
[W/cm
2
]