Why no engine — not even a hypothetical perfect one — can turn heat completely into work, and the one honest upper limit every real engine has to live under.
Two objects are in thermal equilibrium when no net heat flows between them — meaning they're at the same temperature. This sounds almost too obvious to state as a "law," but it's exactly what makes the entire concept of temperature logically sound.
This is precisely why a thermometer works at all: it reaches equilibrium with whatever it's measuring, and by the zeroth law, its reading tells you something objectively true about that object's temperature — not just about the thermometer itself.
Internal energy (U) is the total energy contained within a system — the kinetic and potential energy of all its particles, on the microscopic scale. Unlike heat or work, internal energy is a genuine property of the system's current state, regardless of how it got there. Heat and work are simply two different routes by which energy can be added to or removed from that internal energy store.
The first law is nothing more than energy conservation, applied specifically to heat and work.
Gases need two different specific heats, depending on whether they're heated at constant volume or constant pressure — because at constant pressure, some of the added heat goes into doing expansion work rather than raising temperature.
A thermodynamic process describes how a system moves from one state to another. Several idealised types come up repeatedly:
A heat engine converts heat into useful work by operating in a repeating cycle, absorbing heat from a hot reservoir and rejecting some (never all) of it to a cold reservoir.
A refrigerator is essentially a heat engine run in reverse: instead of producing work from a heat flow, it consumes work to force heat to move from a cold space to a warmer one — something that would never happen spontaneously.
The first law only forbids creating or destroying energy — it says nothing about which energy conversions are actually possible in practice. The second law fills that gap, and can be stated in two equivalent ways:
A reversible process could, in principle, be run backward through exactly the same sequence of states, leaving no net change anywhere in the universe — an idealisation, since it requires infinitely slow, perfectly balanced (quasi-static) changes. Every real process is, to some degree, irreversible — friction, turbulence, and rapid unbalanced changes all generate some permanent, one-directional loss, which is exactly why real engines can never quite reach the theoretical Carnot efficiency below.
The Carnot engine is a theoretical, perfectly reversible heat engine, operating between two fixed temperatures — and it sets the absolute upper bound on efficiency that any real engine, however cleverly designed, can never exceed.
A gas absorbs 500 J of heat and does 200 J of work on its surroundings. Find the change in its internal energy.
Solution: ΔU = Q − W = 500 − 200 = 300 J.
A Carnot engine operates between a hot reservoir at 500 K and a cold reservoir at 300 K. Find its efficiency.
Solution: η = 1 − Tc/Th = 1 − 300/500 = 1 − 0.6 = 0.4 = 40%.
No real engine operating between these same two temperatures could ever exceed 40% efficiency — this is the absolute theoretical ceiling.