Irreversible process Entropie-Change/cylinder

[Abigale]

Hi,

I have read that for an irreversible process the equation for the entropy is: $$ds>\frac{dQ}{T}$$
But if I regard a cylinder connected to a heatreservoir and want to callculate the entropychange of this cylinder, why can I use the equation: $$ds=\frac{dQ}{T}$$?

THX

 

[Chestermiller]

Your inequality applies to the closed system that you are applying the process to. Your second equation is not the entropy change for the material in the cylinder unless the process is reversible, irrespective of the heat reservoir. If you regard the heat reservoir as a system, then the second equation describes its change of entropy, since its temperature is constant and (virtually) uniform, and the heat addition takes place reversibly. The key to inequality vs equality is if the system under consideration is undergoing a reversible change.