The fundamental equation for a closed system

Equation (1 19) is the basic equation for a closed system, i.e. one which does not exchange matter with its environment. It may be derived more directly as foDows. From the first law 

This equation is applicable only when volume change is the only form of work. It is also applicable only to closed systems which are in a state of internal equilibrium,f since all our considerations so far have been based upon these. However, the equation is entirely applicable to a system which changes its composition due to internal chemical reactions, provided that these take place reversibly and also that no work is performed other than that due to volume change. 

Despite what has just been said, the terms TdS and pdF can be identified as the heat absorbed and the negative of the work done on the system respectively, only in the case of a reversible path. Thus we can write 

Finally, it may be noted that in a cyclic process we have 

The work performed in a reversible cycle may thus be obtained either as an area on the P- F diagram or as an area on the T-iSf diagram of the particular substance which passes through the cycle.  

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