[sorin cezar (OP)]

This is a very handy experiment and it can be performed even in a low school laboratory or at home. For the experiment a crucible, some NaCl (preferable reagent grade, but even kitchen salt is good), graphite electrodes, a flame heating source, an ammeter and few 1,5 V batteries are necessary. The difference of setup between the two situations is related only to the voltage of the electrical source. As it can be seen in fig. 1 the circuit consists in a single 1,5V battery and in fig. 2 there are at least 3 batteries connected in series.

Case 1. A 1,5 V battery in circuit
Fill in the crucible with NaCl and then heat it with the burning flame until the NaCl starts to melt. In parallel, follow the indication of the ammeter. With solid NaCl, the current in circuit is zero. As crucible becomes reddish and NaCl starts to melt, an electric current appears into circuit. With a distance of about 2 cm between electrodes, the current into first circuit stabilizes at a value of about 53 mA and the current remain quite stable (small variations between 51 and 55 mA), as far the heating source keeps the NaCl molten into circuit. The current ran into circuit for 2 hours and for all this time the current did not decreased under 50 mA . No smell of gaseous chlorine was detected during this time. After that, the flame was removed, the crucible was left to arrive to the room temperature and distilled water was added to the crucible. The pH of the solution was neutral (checked either with a paper indicator or a common pH meter).

Case 2. At least 3 x 1,5 V batteries in circuit
Perform this part of experiment under a hood or in ventilated space.
Fill in again the crucible with NaCl and then heat it with the burning flame until the NaCl starts to melt. In parallel, follow the indication of the ammeter. With solid NaCl the current in circuit is again zero. As crucible becomes reddish and NaCl starts to melt, an electric current appears again. With the same distance between electrodes, the current into circuit stabilizes at a value of about 65 mA and the current remain quite stable (small variations between 62 and 67 mA) as far the heating source keeps the NaCl molten into circuit. After few minutes, you will feel a characteristic smell of chlorine. Turn the ventilation on and leave the current to flow for another few minutes, then disconnect the batteries and remove the flame. Leave the crucible to arrive at room temperature and with care, add some distilled water.  A reaction takes place in the crucible and the reaction is quite violent. The solution has a basic character due to NaOH formation, and this can be very easily checked with a pH indicator. 

 How can we interpret the experiment?

If melted NaCl is formed by ions, there is no possibility to discharge these ions at electrodes at a voltage lower then 4 V. In the first case the electrolytic cell should comport like a capacitor and after short interval of time the current in circuit must decrease to zero.
 The following equation represents the breaking apart of NaCl(l):
2NaCl(l) → 2Na(l) + Cl2 (g)
The half-reactions involved in this process are:
Reduction: 2Na+(l) + 2e- → Na(s) E° = -2.71 V
Oxidation  2Cl-(l) → Cl2 (g) + 2 e-   E° =-1.36V

net voltage required = - 4.07V
The negative sign of voltage tells us that the overall reaction will NOT be spontaneous, and a minimum of 4.07 volts will be required for this reaction to occur.

The chemical effects at electrodes again cannot be explained by actual  science. In the first case, the quantity of electricity passing through circuit was at least ten times greater then in the second case, but … no chemical effect was detected.   

The experiment is dedicated for those who hardly tried to explain how electrolysis of NaCl takes place at any potential or electric current have at least  least 4  possibilities to flow into a circuit and not generate an chemical effect ...

[alancalverd]

As before, you have failed to understand the difference between ionic mobility and electrolysis, even though you have demonstrated it.

[CliffordK]

Does a molten salt (ionic compound) undergo electrolysis like water does?  Perhaps it is a slightly different process that is forcing the ions to recombine to form chlorine gas. 

It does sound like an interesting way to purify sodium.

[alancalverd]

If the voltage is high enough, yes. It's the standard procedure for extracting aluminium.

[sorin cezar (OP)]

Does a molten salt (ionic compound) undergo electrolysis like water does?  Perhaps it is a slightly different process that is forcing the ions to recombine to form chlorine gas. 

It does sound like an interesting way to purify sodium.

I did not know there are other processes in case of molten salts...
Are these processes described somewhere?
Alkali metals were obtained by this method few centuries ago ... and this is not the topic of the experiment...