Re: condensation of gas clouds into a star violate the 2nd law of thermodynamic

The most convenient form for the second law of thermodynamics (to 
answer your question) is:

"In an ADIABATICALY ISOLATED thermodynamical system the entropy will 
increase in any real (irreversible) process".

From this, it is obvious that the second law doesn't say anything 
about the evolution of open system, as is a gas cloud in space. We 
notice, as you did, that for the process of condensation of cosmic 
gas into a star the entropy decreases. We also know that:

T*dS = dQ, and T>0

Therefore, it must be that energy is radiated as heat. This effect 
can be observed. The same line of reasoning could also be used to 
show that matter falling into a black hole would emit energy as 
termic radiation. This is a way of detecting black holes.

Also, see the answer to question 907687350.Ph