Elementary and matter-radiant working bodies

Two types of working body are considered:

• Elementary working body – matter or radiation in one cycle;

• Matter-radiant working body – matter and radiation in one cycle.

3.1 Energy conversion without irrevocable losses

According to Carnot theorem, an efficiency of a Carnot engine does not depend on a chemical nature, physical and aggregate states of a working body. The work presents a peculiarity of applying this theorem for solar cells. The statement is that the maximal efficiency of solar cells can be achieved with help of a combined working body only. Let’s consider it in detail.

For example, the maximal efficiencies of the solar energy conversion are equal 94.8% at the limit temperatures 300 K and 5800 K (yOS in the Table 1). Under these temperatures the efficiencies of the solar energy conversion can be equal 5.91% (nOyC in Table 1). The one belongs to a Carnot cycle, in which a matter and radiation are found as a combined working body, i. e. matter and radiation as a whole system. The other belongs to 2 cycles running parallel. A matter performs the work with a low efficiency 6.25% (yO in Table 1), but the radiation performs the work with a high efficiency 94.5% (yC in Table 1). In these cases matter and radiation are elementary working bodies. The efficiencies of these parallel processes is

П0Пс = 0.948 * 0.0625 = 0.0591 = 5.91%.

Table 1 shows that a matter performs the work with a low efficiency in solar cells. However, the efficiency of the radiant work at the same absorber temperature is considerably higher. For example, a radiation performs the work with efficiency 92.6% during a non-Carnot cycle (yAS in Table 1), but a matter produces work only with an efficiency 6.25% (y0 in Table 1) at the absorber temperature 320 К. This difference is caused by various limit temperatures of the cycles (Table 1). The efficiencies of these processes running parallelis smaller than that of ЦаЦс – n^As = 0.926 * 0.0625 = 0.0579 = 5.79%.

However, at the same temperatures the efficiency of solar energy conversion achieves 94.8% (yOS in Table 1), if a work is performed during a cycle with the matter-radiant working body.

Classification of engines

Efficiency at Ta = 320 K and other parameters of cycles

Cycle

Working

body

Limit tempe­ratures^

Symbols

Limit,

%

Calcilated

equation

Carnot engines

heat

Carnot

Elementary / matter or radiation

300-320

П0

6.25

2

solar

Carnot

elementary

320-5800

nC

94.5

3

ideal solar – heat

Carnot

matter-radiation / matter and radiation in one cycle

300-5800

yos

94.8

4

non-Carnot engines

solar

non-Carnot

elementary

320-5800

nAS

92.6

5

solar – heat

non-Carnot

matter-radiation

300-5800

___ nL__

93.1

6

combined engines

combined

Carnot,

Carnot

elementary

300-320

320-5800

y0yc

5.91

2,3

combined

Carnot

Carnot

elementary

300-320

300-5800

y0yos

5.93

2,4

combined

Carnot, non – Carnot

elementary

300-320

320-5800

y0yAS

5.79

2,5

combined

Carnot, non – Carnot

elementary

300-320

300-5800

n$nc

5.82

2,6

Table 1. Classification and efficiencies of the engines with the elementary and matter-radiant working bodies

A Carnot cycle with the efficiency nos and the matter-radiant working body has been considered by the author earlier in the chapter, its efficiency is given by eq.4. Further we will call an engine with the matter-radiant working body an ideal solar-heat one. The elementary working bodies perform the work by solar or heat engines. Their properties are listed in Table 1. The advantage of the cyclic processes in comparison with the matter-radiant working body is obvious.

So, the elementary working bodies perform the work with the efficiencies По, По nL and nAS. The matter-radiant working bodies perform the work with the efficiency nOS. According to the Table. 1, one can confirm:

– a Carnot cycle with the matter-radiant working body has a maximally possible efficiency of solar energy conversion. It is equal 94.8% and does not depend on absorber temperature TA. Engine where work is done during such cycle we will call an ideal solar-heat engine.

– electrical energy can be obtained under operating an ideal heat-solar engine with a very high efficiency and without additional function of low efficiency heat engine.

Therefore, high efficiency solar cells should be designed as solar-heat engine only.