Relation between Pressure and volume in adiabatic process? Why in adiabatic 
compression and expansion small volumetric change occurs while in isothermic compression or expansion very small pressure is applied and volume changes very significantly i am referring to PV diagram of Carnot engine?
 A: In Adiabatic changes the system is disconnected from the surrounding therefore any change in pressure leads to work which  goes to change in internal energy of the system -
this change is reflected as change in temperature (one can visualize it as change in kinetic energy of the gas molecules)
 so the amount of work done does not lead /can not lead to large volume changes. If large volume changes will occur then the Kinetic energy can  not rise to the extent demanded
The change in pressure is related to  change in volume raised to a power gamma where  gamma is greater than 1.0
In Isothermal  situation ,the  system is in thermal contact with the surrounding and the change in pressure  leads to  work done which can be exchanged as heat energy with the surrounding -
the internal energy remains the same so  change in pressure is related inversely to the  change in volume only  . The thermal energy can  come inside or can go from the system to the surroundiing - mechanical work  is the p.dv amount.
In any engine running between two resevoirs  the importance of isothermal and adiabatic parts can be underlined to say that the  conversion of heat  into mechanical work is done  during the adiabatic paths whereas the isothermals are regions to draw energy  or throw it out to the surroundings.
