How is a work done in a free expansion process?

First law of thermodynamics states that cyclic integral of heat transfer is equal to cyclic integral of work.transfer but it is valid for slow or moderate process, free expansion is a very fast process, so theoretically work transfer is considered as zero

zero,as change in heat and change in internal energy is zero,then by first law of thermodynamics work become zero.

Work done in free expansion is zero because the process is highly irreversible.