What is the definition of entropy in the context of thermodynamic processes?

A gas absorbs 500 J of heat during an isothermal expansion at 300 K. Calculate the change in entropy of the gas.

Calculate the change in entropy when 100 grams of ice at 0°C melts into water at 0°C. (Latent heat of fusion of ice = 334 J/g)

Determine the change in entropy when 2 kg of water is heated from 20°C to 80°C. (Specific heat capacity of water = 4.18 J/g°C)

An underlying theory suggests that in any given process, the quantity of energy that becomes inaccessible (or lost) for doing useful work equals $T_L\Delta S$, where $T_L$ signifies the lowest accessible temperature and $\Delta S$ denotes the total change in entropy throughout the process. Determine the expression for the lost energy E_lost for the free adiabatic expansion that occurs inside of an idealized gas.