[Mr.A]

pv graph of a carnot cycles is above..
My question is the C to D step it says that its a adiabatic compression.. so why there no significant change of the volume in the x axis in moving C to D? 

and i know that step is reversible and the reversible processes take an infinite amount of time... But to make this happen adiabatically, dont we have to do that process very fast ? If not , how it is possible to stop the heat change ? I may have missed out something but Id be really grateful if someone could clear this out...  

[mjc123]

That is not the graph of a Carnot cycle. C-D as drawn is not an adiabatic compression but an isovolumetric heating. Likewise A-B is an isovolumetric cooling when it should be an adiabatic expansion. Reversible adiabatic expansion/contraction follows a curve PV^γ = constant, where γ = C_p/C_v. T will of course change during this process.

[TyPie]

Adiabatic assumptions are used when there is very little temperature change over a very short time in the practical sense.

[curiouscat]

But to make this happen adiabatically, dont we have to do that process very fast ? If not , how it is possible to stop the heat change ?

Not necessarily. Just use insulation.