Second Law of Thermodynamics

The second law of thermodynamics states that no heat engine can be more efficient than a reversible heat engine working between two fixed temperature limits (Carnot cycle) i.e. the maximum thermal efficiency is equal to the thermal efficiency of the Carnot cycle:

or in other words If the heat input to a heat engine is Q, then the work output of the engine, W will be restricted to an upper limit Wmax i.e.

It should be noted that real cycles are far less efficient than the Carnot cycle due to mechanical friction and other irreversibility.

The second law of thermodynamics (the entropy law or law of entropy) was formulated in the middle of the last century by Clausius and Thomson following Carnot's earlier observation that, like the fall or flow of a stream that turns a mill wheel, it is the "fall" or flow of heat from higher to lower temperatures that motivates a steam engine. The key insight was that the world is inherently active, and that whenever an energy distribution is out of equilibrium a potential or thermodynamic "force" (the gradient of a potential) exists that the world acts spontaneously to dissipate or minimize. All real-world change or dynamics is seen to follow, or be motivated, by this law. So whereas the first law expresses that which remains the same, or is time-symmetric, in all real-world processes the second law expresses that which changes and motivates the change, the fundamental time-asymmetry, in all real-world process. Clausius coined the term "entropy" to refer to the dissipated potential and the second law, in its most general form, states that the world acts spontaneously to minimize potentials (or equivalently maximize entropy), and with this, active end-directedness or time-asymmetry was, for the first time, given a universal physical basis. The balance equation of the second law, expressed as S > 0, says that in all natural processes the entropy of the world always increases, and thus whereas with the first law there is no time, and the past, present, and future are indistinguishable, the second law, with its one-way flow, introduces the basis for telling the difference.