For a gas transformation to be reversible, the gas must remain infinitesimally close to equilibrium throughout the whole process. It is not enough for the initial and final states to be equilibrium states: every single intermediate instant must be too. This is a strict requirement, which splits into two distinct conditions that must be satisfied simultaneously.
The first is thermal equilibrium: the temperature of the gas must be equal — or differ by at most an infinitesimal amount — from that of the reservoirs with which it exchanges heat. If there were a finite temperature jump between the gas and the reservoir, heat would flow spontaneously from hot to cold and generate entropy, making the process irreversible.
The second is mechanical equilibrium: the pressure of the gas must be equal — or differ by an infinitesimal amount — from the external pressure acting on the piston. If the internal pressure were to exceed the external one by a finite amount, the gas would push the piston abruptly and uncontrollably, again producing entropy.
Note
A reversible transformation is always infinitely slow: at every instant the gas is in equilibrium. This is the price to pay so that not even a finite jump in temperature or pressure ever appears.
In depth — How this is achieved in practice
A reversible transformation is achieved in practice by using infinitely many reservoirs at progressively different temperatures, so that the gas moves from one temperature to the next always in contact with a reservoir almost identical to its own state. For pressure, imagine adding grains of sand one at a time onto the piston, changing its load so gradually that the gas is never pulled away from mechanical equilibrium. In reality, reversible processes are a useful idealisation: no real process is perfectly reversible, because every transformation that takes place in finite time generates a little entropy.
Connections
Topics: Thermodynamics Concepts: Thermodynamic transformations · Second law of thermodynamics Objects: Ideal gas · Piston and cylinder
Related exercises: Worked exercise — reversible vs irreversible isothermal expansion · Problem — True or false about reversibility and cycles · Worked exercise — free expansion is not reversible