Question

An ideal gas is compressed to 10 times its initial pressure. Thefinal volume is smaller for (an isothermal compression). Why?

1 mol of hot water mixes adiabatically with 1 mol of cold water.The entropy change of the cold water is 0.21 J/(molK). Why is theentropy change of the hot water greater than -0.21 J/(molK)?

You raise the pressure of a gas at constant temperature in aclosed, adiabatic system. Why does the entropy of the gas decreaseinstead of staying the same since there is no heat added and it'sisothermal?

I know the answers to all of these, but I don't understand thewhy's. Any help will be greatly appreciated.