[Ahmed Abdullah]

1.I have found this about an irreversible process,
"An irreversible process is one in which the intermediate states cannot be specified by any set of macroscopic variables and which are not equilibrium states. Since the intermediate states are unknown this process cannot be reversed."

why this intermediate states cannot be specified by any set of macroscopic variables?

We know the relationship among this variables - which let us know how change in one variable affects the other. So I think we can definitely work out the inter-mediate state ( in terms of these variables).

2. "A reversible change in thermodynamics is a change that can be reversed by an infinitesimal modification of a variable."

Why "infinitesimal modification" is set as a requirement for a reversible process.

Suppose a gas cylinder is in equilibrium (the cylinder is completely insulating). Now, we put a weight on the piston ( frictionless one). The gas compress adiabatically. Let's say the change in volume is V (substantially large). Temperature increases after the process (i.e increase in internal energy). Now just remove the weight,  what happens? I think the gas retain its initial condition. It expand ,completely losing the energy it gained before. It came back to original state! So it should be a reversible process though it doesn't fullfill the requirement -infinitesimal change in variable.
Any input should be appreciated.

[Valdorod]

A reversible change in thermodynamics is a change that can be reversed by an infinitesimal modification of a variable

Actually, if I am not mistaken it should be "an infinitesimal modification of the driving variable"

In the example you provided, any small change in the mass applied to the piston (infinitesimal decrease in mass) would begin the reversible process.  Thus your example does meet the requirement.

Valdo

[Ahmed Abdullah]

when i put the weight on the piston there is an instant change of pressure mg/A , which is not infinitesimal. Still the process is reversible.

Could you give example of some irreversible processes?

[Structuralist]

1.I have found this about an irreversible process,
"An irreversible process is one in which the intermediate states cannot be specified by any set of macroscopic variables and which are not equilibrium states. Since the intermediate states are unknown this process cannot be reversed."

why this intermediate states cannot be specified by any set of macroscopic variables?

Firstly there are several definitions about reversible/irreversible process.

The intermediate states cannot be defined, this can be shown mathematically but you can conclude the point by this example. If we have a clip separated in two parts, in the first one let we have an gas and in the second one vacuum. If we break the wall between, the volume will increase. Now let imagine the intermediate state, the gas molecules are moving chaotically and because of that the pressure (for instance) will be different in different parts of the clip , and that so we can not define this intermediate state.
But if the process is reversible the change of the volume (for instance) in every time is infinitely small (kvasy static) and that so we can express the intermediate state.
I hope that I helped   

[Valdorod]

As Structuralist said there are several definitions of reversible processes.

From the definition you are providing, you are talking about reversible P-V work.  The reversible processes is an idealization to begin with and in practice any large sudden change in the driving variable will lead to an irreversible process.

In other words just because a reaction is reversible or a process is reversible, it does not mean that it is "Reversible P-V Work".

Once again as Structuralist mentioned in his example, "because the pressure will be different in different parts of the clip, the intermediate state cannot be defined thermodynamically.  The example given by Structuralist is a good example of irreversible work.  It really comes down to technicalitites.

Valdo

[Ahmed Abdullah]

1.I have found this about an irreversible process,
"An irreversible process is one in which the intermediate states cannot be specified by any set of macroscopic variables and which are not equilibrium states. Since the intermediate states are unknown this process cannot be reversed."

why this intermediate states cannot be specified by any set of macroscopic variables?

Firstly there are several definitions about reversible/irreversible process.

The intermediate states cannot be defined, this can be shown mathematically but you can conclude the point by this example. ....I hope that I helped   

Yes it really helped me. Now i really want to know the mathematical part of it. Could anyone please show it?

[Ahmed Abdullah]

ops

[Structuralist]

Well thats when you will attend postgraduate studies of physical chemistry 

Thermodynamically and macroscopic this is OK, this kind math is mostly needed for molecular level,
up to then you can continue with learning of the basics and one day you will work it out. The most important thing is to have will to do that. 

p.s I'm just a basic physical chemistry student too