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Why is the change in any state function ...

Why is the change in any state function in a cyclic process zero? Is the change in any state function for both reversible and irreversible cyclic process zero?

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The vlaue of any state function of a system depends only on the present stae of the system. In a cyclic process, the initial and the final states of a system are the same, so are the values of a state function at these two states. Hence, the change in a state function will be zero in a cyclic process. The change in any state function depends only on the initial and the final states of the system. it does not depend on the path followed to carry out the change. This means that a state function undergoes the samme change in a process with the specified initial and final stetes irrespective of of whether the process is carried process, the change in any state function is always zero. hence, for both a reversible and an irreversible cyclic process, the change in any state function will be zero.
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