The Second Law & Reversibility

A hot cup cools in a cold room; it never spontaneously warms up while the room cools. Energy would be conserved either way. Something else decides which way nature goes: the second law.

Processes that only go one way#

• Bodies at 100°C and 0°C in contact both end at 50°C. Two bodies at 50°C never become one at 100°C and one at 0°C.
• A sliding block stops, warming itself and the table. A warm block never cools down and starts sliding.
• Gas let into an empty chamber fills both halves. It never gathers back into one half by itself.

None of the reverse processes would break the first law. Another law must decide which processes actually happen.

The Kelvin–Planck statement#

An engine with Q₂ = 0 would be 100% efficient. It would need no cold body: it could take heat from one body at one temperature, even the surroundings, and turn it all into work. A ship could run on the warmth of the ocean, a scooter on the warmth of its own body. All attempts failed:

Reversible and irreversible processes#

Quasi-static processes

A gas is in thermodynamic equilibrium when a single p, V and T describe the whole of it. Heat it on a stove and different parts have different temperatures, so it isn’t. A quasi-static process is carried out so slowly that the system is always very nearly in equilibrium, so it can be drawn as a curve on a p–V diagram. Real processes only approach this.

Reversible processes

A process from i to f is reversible if it can be run backwards along the same curve, with every small part exactly undone: the heat taken in on the way out is returned, and the work done is done back on the system. That needs two things:

• it must be quasi-static, and
• it must be non-dissipative: no friction, viscosity or similar losses.

A cyclic process whose every part is reversible is a reversible cycle. From here on, processes are assumed reversible unless stated otherwise.