Power Plant Engineering

80 POWER PLANT ENGINEERING

Above absolute zero temperature, some electrons may have energies higher than the Fermi level.
The energy that must be supplied to overcome the weak attrac-tive force on the outermost orbital
electrons is the work function, Φ, so that the electron leaving the emitter has an energy level Φ + εf.
When emitter is heated, some high energy free electrons at the Fermi level receive energy equal to
emitter work function Φc, and escape the emitter surface. They move through the gap and strike the
collector. The K.E. (εfa) plus the energy equal to collector work function Φa is given up and this energy
is rejected as heat from the low temperature collector.
The electron energy is reduced to the Fermi energy level of the anode εfa This energy state is
higher than that of the electron at the Fermi energy level of cathode εfc. Therefore, the electron is able
to pass through the external load from anode to cathode. The cathode materials are selected with low
Fermi levels as comprised to anode materials which must have higher Fermi level.

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 Φa.
Potential barrier,
Vc > Φc and Vc > Φa
The current densities are :

Jc = A 1 Tc^2

c

c

V

e kT

−

 [A/cm^2 ]

Ja = A 1 Tc^2 2

Vc

e kT

−



[A/cm^2 ]

The output voltage across the electrical resistance R,

Vo = Vc – Va = φc – φa =

1

e

(εfa – εfc)

Each electron has to overcome the interspace potential (Vc – Φc) and work function Φc when it
leaves the cathode. The net energy carried,

Q 1 c = Jc (Vc – φc + φc) = Jc Vc [W/cm^2 ]

Fig. 2.26. Characteristic Curve.

Elc

Vcφc

φa

δ V

a

Vo

Ela

Gap Distance

Energy Volts (–)