A possible case of an irreversible process in which total entropy decreases

[ticktock]

When a hot stone is dropped into a lake the change in temperature of the lake is negligible, but the stone cools down and so its entropy decreases. Is this therefore a case of an irreversible process in which total entropy decreases?

This isn't for homework but for revision towards my resit. I just can't find anything in my notes which is helping me understand.

 

[Mapes]

Hi ticktock, welcome to PF. No, this is not an example of total entropy decreasing. The entropy increase in the lake is finite (and greater than the entropy decrease in the stone) even if you consider the temperature increase in the lake to be negligible.

 

[vela]

When an amount of heat |dQ| moves from the stone to the lake, the decrease in entropy of the stone is$$dS_\mathrm{stone} = -\frac{|dQ|}{T_\mathrm{stone}}$$ and the increase in entropy of the lake is $$dS_\mathrm{lake} = \frac{|dQ|}{T_\mathrm{lake}}$$The total change in entropy is dS = dS_lake+dS_stone. Given the relative temperature of the lake and stone, what can you say about the sign of dS? Does assuming T_lake is a constant make a difference?