the following pics are taken from resnick halliday fundamentals of physics . They clearly say that the entropy change of the system for an irreversible process between two equilibrium states i and f (say) will be same as that for a reversible process between the same two states.This is because entropy being state function depends only on the initial and final states...and for convenience we write it as equal to that for the reversible process..as dS system = [i ] [f ] (dQ r / T)........where dQ r is the heat taken by the system in the reversible process. Now they again say that total entropy change of system and surrounding for a reversible process will be zero and that for an irreversible process will be greater than zero. The first part is clear... if in a reversible process system absorbs heat dQ r ,then surrounding also loses the same heat . So dS surrounding for reversible process = - [i ] [f ] (dQ r / T) So dS universe (reversible process) = dS system + dS surrounding = [i ] [f ] (dQ r / T) - [i ] [f ] (dQ r / T) = 0 Now how should i define dS surrounding (for irreversible process) such that dS universe (irreversible process) = dS system + dS surrounding > 0 __________________________________________________________________ It is to be noted that dS system = [i ] [f ] (dQ r / T) for both reversible and irreversible process as entropy of the system is a state function and does not depend on the path followed (read the passages) __________________________________________________________________

the following pics are taken from resnick halliday fundamentals of physics.

 

They clearly say that the entropy change of the system for an irreversible process between two equilibrium states i and f (say) will be same as that for a reversible process between the same two states.This is because entropy being state function depends only on the initial and final states...and for convenience we write it as equal to that for the reversible process..as

dS_system = _{[i ]}^{[f ]} (dQ_r / T)........where dQ_r is the heat taken by the system in the reversible process.

 

Now they again say that total entropy change of system and surrounding for a reversible process will be zero and that for an irreversible process will be greater than zero. 

 

 

 

The first part is clear...

if in a reversible process system absorbs heat dQ_r ,then surrounding also loses the same heat .

So dS_surrounding for reversible process = - _{[i ]}^{[f ]} (dQ_r / T)

So dS_universe(reversible process)

= dS_system+ dS_surrounding = _{[i ]}^{[f ]} (dQ_r / T) - _{[i ]}^{[f ]} (dQ_r / T) = 0

 

Now how should i define dS_surrounding(for irreversible process) such that

dS_universe(irreversible process) = dS_system+ dS_surrounding  > 0

 

__________________________________________________________________

It is to be noted that dS_system = _{[i ]}^{[f ]} (dQ_r / T) for both reversible and irreversible

 

process as entropy of the system is a state function and does not depend on

 

the path followed   (read the passages)

__________________________________________________________________