thermodynamics....entropy wrt carnot cycle

[abvegto]

 

here is a representation of the carnot cycle in the pv diagram(y=p x=v)...

 

we kno that entropy is defined as the measure of randomness of a system.....

 

from the veiw point of kinetic theory the entropy change during an adiabatic process is zero since q = 0( bc or da)for an ideal gas......but during the process there is an increase in the randomness of the system i.e there is an increase in the volume of the system..

does this increase in volume account for any change in entropy for a real gas? if yes then how to measure it?...

 

D U = (dU/dT _v) dT + (dU/dv _T) dV.....in case of a real gas can we write the change in entropy as ds = dU/dT?....

plz help...