Q4. A paddle does 500 J of work stirring water that is in thermal contact with a large reservoir, and the water’s temperature stays the same. Where does the energy go, and why can the process not be reversed exactly?
The 500 J becomes internal energy and passes as heat into the reservoir. Reversing it exactly would take 500 J of heat from the reservoir and turn it all into work with no other change, which the Kelvin–Planck statement forbids.
Q5. Is the melting of ice at 0 °C (at 1 atm) reversible? Under what conditions?
Only in the ideal limit: if the surroundings are at 0 °C plus an infinitesimal amount, the ice melts quasi-statically and lowering the surroundings infinitesimally below 0 °C would refreeze it. Ice melting in a warm room, across a finite temperature difference, is irreversible.
Q6. Why is reversibility important for heat engines?
An engine using only reversible processes has the highest efficiency possible between two reservoirs at given temperatures. Any irreversibility, such as friction or heat flow across a finite temperature difference, lowers the efficiency below that limit.