[AdiDex]

What happens  if we heat it..??
I thought H₂O will eliminate ....and anhydride will form but then i realised the anyhydride which is forming , have 4 membered ring so it can't be a major product.
So now what i think this product should be major product am i right ...??

What i think that anhydride formation occurs preferably in acidic medium ..otherwise CO₂ get eliminated...am i right..?

I have  some doubts
1. I want to show my mechanism but i don't know how to show . anyway i am trying to
write . first C-C bond will undergo homoletic cleavage then O-H  bond and CO₂ will form , Now we have H·  , it can combine with C· and the product will be . Is this mechanism is appropriate ..?.

2.  Can H· attack on C-H bond to form H₂ and   ...is this our major product...??

3. What will happen if we just heat a compound having O-H bond ..This bond will undergo which cleavage either homoletic or heteroletic ...? (No acidic medium or basic medium is given)

[TheUnassuming]

I think generally you are on the right track, though be careful as most of the time you will get heterolytic cleavages vs homo in mechanisms you encounter.  The exception to this is if the reaction conditions include explicit radical conditions like light or chemical radical initiators. 

Formation of the anhydride seems unlikely if you are just heating the substrate. 

Try starting with deprotonation of one of the carboxylic acids (imagine perhaps it protonates the carbonyl of the other carboxylic acid).

[Enthalpy]

I had imagined that two or more diacids would join to make the anhydride together, as a cyclic dimer or an oligomer. Or wouldn't they? Hum, I'm leaning far out of my knowledge window here.

Like that:

[AdiDex]

Like that:

I think it will not be the major one....because in this reaction 2 molecules are reacting so it will be less probable.....moreover it is entropy disfavoured .
When we heat drastically may be it will form in bery less quantity.
I don't know whether it is correct or not.this my opinion.

[TheUnassuming]

In general when I see two carboxylic acids coming off the same carbon and see energy being put into the system I assume there will be a decarboxylation event of some manner. 

[Enthalpy]

Thanks, +.
And my apologies for having put nonsense.

[TheUnassuming]

Thanks, +.
And my apologies for having put nonsense.

haha... no apologies.