Question

How is work of compression least in isothermal process?

Answer 1

Work done in an Isothermal compression process is given by 
    
   W = n R T Ln (V2 / V1) ,            as   P 1 V1 = P2 V2 = n R T.

Let us say that a gas is compressed with pressure and temperature both allowed to vary.  When a gas is compressed the molecules become closer. They collide with the walls more frequently. So the pressure increases. Also due to this action the temperature of the gas increases too.  So there is an increases in the internal energy.  
  
    So work done  = work done for compression + increase in internal energy.

      Change is internal energy is dependent solely on the initial and final temperatures or, their difference.

  Increase in internal energy is zero when a gas undergoes an isothermal expansion or compression.  So then work done is the least.

Answer 2

Intuitively I would assume that the isothermal work is usually lower than the adiabatic work, as compression lowers the volume of the system and therefore usually increases the temperature if heat exchange with the surroundings is not allowed. Isothermal compression requires heat transfer to the surroundings to maintain constant temperature, lowering the pressure of the system and thus lowering the resistance to compression compared to the adiabatic compression (where heat exchange is not allowed).