Question about Greatest Work

[Sylvia Zhang 2L]

Why is it that the greatest work done on a system is for a reversible reaction? And why is it important?

[Ankit Budhiraja 3D]

The primary reasoning behind the greatest work being done on a system occurring in reversible reactions seems to be due to minimal heat being lost to the surroundings, thus implying greater work being exerted on a system. This is important because deltaS can't be calculated using the general equation for cases of reversible reaction due to the minimal amount of energy being lost as heat and rather larger amounts of work being exerted upon the system.