Consider two systems, each containing an ideal gas with N particles kept at the same temperature, but different pressures P1 and P2. After reservoirs are combined together what is the change of the entropy? Try to solve this problems in few steps:
-By using equation of state for the ideal gas determine the pressure P after mixing.
-Use Sackur-Tetrode formula together with the ideal gas equation of state and express entropy in terms of temperature, number of particles and pressure.
-Find now entropy in the initial and final states and eventually compute difference between them.