What is entropy?

Provide the mathematical equation for entropy change.

The entropy change,in the conversion of one mole of liquid water at $373 \, K$ to vapour at the same temperature is (Latent heat of vaporization of water,$\Delta H_{vap} = 2.257 \, kJ/g$) ........ $J \, K^{-1}$ (in $.9$)

An engine operating between $150\,^{\circ}C$ and $25\,^{\circ}C$ takes $500\,J$ of heat from a higher temperature reservoir. If there are no frictional losses,the work done by the engine is.....$J$.

For a reversible spontaneous change,$\Delta S$ is:

What is the entropy of vaporisation of water at $100\,^{\circ}C$,if the molar heat of vaporisation is $9710\,cal/mol$?