# Why doesn't entropy get decreased in adiabatic expansion process?

I was reading the second step of Carnot cycle in which the system undergoes adiabatic expansion doing work & thus decreasing the internal energy of itself. The entropy didn't change as no further heat energy was supplied or taken out; it remained the same as it was after the first step of the cycle that is $\Delta S = \frac{Q_\text{isothermal}}{T}.$

However, I wonder why wouldn't the disorder of the system decrease after the adiabatic expansion; the system is doing work & is losing its internal energy with fall in temperature . Wouldn't this decrease the randomness or disorder of the system after-all it is now less energetic? And doesn't less energetic mean lesser number of microstates & lesser disorder in the system? So, why should the entropy which is the measure of the disorder changes?

• @Mark Mitchison: Entropy is not disorder. I'm not using the word disorder like that attributed to messy desks or shuffled cards etc.; what I mean is simply the number of microstates; that's it. – user36790 Nov 11 '15 at 2:56