Q.Explain reversible and irreversible processes. Describe the working of Carnot engine. Obtain an expression for the efficiency.

Reversible processes are idealised and exactly undoable; irreversible processes are real and cannot be perfectly undone. The Carnot engine is the ideal reversible heat engine, with efficiency η = 1 − T₂/T₁ — the theoretical maximum for any engine working between those two temperatures.

Reversible process: A process is reversible if it can be carried out in such a way that, at the end, both the system and its surroundings can be restored exactly to their original states, with no trace left behind. A reversible process must proceed through a continuous succession of equilibrium states (quasi-static), infinitely slowly, with no dissipative effects such as friction, viscosity, or unrestrained expansion. Reversible processes are an idealisation — no real process is perfectly reversible, but some (like a very slow, frictionless, ideal-gas compression) can closely approximate one.

Irreversible process: A process is irreversible if it cannot be exactly reversed — that is, the system and surroundings cannot both be brought back to their original states without some external intervention leaving a permanent change somewhere. All real, naturally-occurring processes are irreversible, because they involve friction, viscosity, finite temperature/pressure differences, or free (unrestrained) expansion. Examples: heat flowing from a hot body to a cold one, gas expanding freely into a vacuum, a pendulum slowing down due to air resistance.

The Carnot engine:

The Carnot engine is an idealised heat engine that operates in a cycle between two heat reservoirs — a hot source at temperature $T_1$ and a cold sink at temperature $T_2$ ($T_1 > T_2$) — using only reversible processes, making it the most efficient engine theoretically possible between those two temperatures. Its working substance (usually taken as an ideal gas) undergoes a cycle of four reversible steps:

1. Isothermal expansion at $T_1$: the gas absorbs heat $Q_1$ from the hot reservoir and expands, doing work, while staying at constant temperature $T_1$.
2. Adiabatic expansion: the gas expands further with no heat exchange, so its temperature drops from $T_1$ to $T_2$.
3. Isothermal compression at $T_2$: the gas is compressed while releasing heat $Q_2$ to the cold reservoir, staying at constant temperature $T_2$. …