The final volume of a system is equal to the initial volume in a certain process. Is the work done by the system necessarily zero? Is it necessarily nonzero?
Work done by the system is neither necessarily zero nor nonzero when the final volume is equal to the initial volume.
Explanation
We know that,
Work done = force ×displacement
Volume = area ×displacement
Therefore,
Work done=pressure ×volume
Let change in the volume of system = ΔV = V2-V1
Pressure =P
Thus, work done by the system W at constant pressure
W=PΔV
But if V2=V1 then, ΔV=0
Work done by the system W=0
So, in an isobaric process (where pressure remains constant) work done by the system will be zero if initial and final volume are equal.
But we also know that in the cyclic process the system returns to its initial state. But still work done is not zero. In fact, in the cyclic process since the system returns to its initial state, internal energy becomes zero. This is because internal energy is a state variable. It depends on initial and final state only. And if initial and final state becomes equal, then change in internal energy will be zero.
According to First law of thermodynamics,
ΔQ=ΔU+ΔW
Where ΔQ=heat supplied to the system
ΔU=change in internal energy
ΔW=work done by the system
In cyclic process ΔU=0.
So, from the first law of thermodynamics ΔQ=ΔW i.e. heat supplied to the system is converted entirely into work in a cyclic process.