According to Second Law of the thermodynamics how much will be the efficiency of heat engine ?

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Correct — option (4), "Less than one". A heat engine takes in heat Q_H from a hot reservoir, converts part of it into work W, and rejects the remainder Q_C to a cold reservoir. Its thermal efficiency is the fraction of the heat supplied that comes out as work: η = W/Q_H = (Q_H − Q_C)/Q_H = 1 − Q_C/Q_H Read that expression and the answer is already visible. The efficiency would equal one only if Q_C were zero — that is, only if the engine rejected no heat at all and turned every joule it absorbed into work. The second law of thermodynamics says precisely that this cannot happen. In the Kelvin-Planck statement, no process is possible whose sole result is the complete conversion of heat drawn from a single reservoir into work. Some heat must always be discarded to a colder body, so Q_C is strictly greater than zero, so η is strictly less than one. The same conclusion comes out of the Carnot limit. For an engine working between reservoirs at absolute temperatures T_H and T_C, the maximum attainable efficiency is η = 1 − T_C/T_H, and no engine operating between those two temperatures can beat it — that is Carnot's theorem. Efficiency reaches one only if T_C is absolute zero or T_H is infinite, and neither is attainable; the third law of thermodynamics itself rules out reaching absolute zero in any finite number of steps. So the ceiling is always below unity, and a real engine, being irreversible, falls further below it again. The cleanest way to hold the two laws together is by what each forbids. The first law is conservation of energy, and it forbids getting out more work than the heat put in — efficiency greater than one is impossible, which is a perpetual motion machine of the first kind. The second law forbids getting out exactly as much work as the heat put in — efficiency equal to one is impossible, which is a perpetual motion machine of the second kind. The old formulation catches it: the first law says you cannot win, and the second says you cannot even break even. That also tells you what the question is really testing. Options (1) and (2) are excluded by the first law and by the definition of efficiency; only option (3) and option (4) are candidates, and the entire content of the second law here is that (3) is unattainable and (4) is the correct description. A candidate who can name what each law forbids does not need the formulae at all. Real engines sit well below the Carnot ceiling. A petrol engine converts roughly a quarter to a third of its fuel energy into useful work, a diesel engine somewhat more, a conventional steam thermal power station in the region of a third to two-fifths, and a modern combined cycle gas plant approaches three-fifths. In every case most of the energy leaves as waste heat — which is not a failure of engineering but the second law showing itself in the exhaust pipe and the cooling tower.

Why the other options are wrong — (a) Option (1) confuses a prohibition with a prediction. The second law places an upper bound on the efficiency of a heat engine; it does not assert that the efficiency is zero. An engine of zero efficiency would deliver no work at all, which describes a broken machine rather than a law of nature — and real heat engines plainly do work, driving vehicles and generators every day. Zero efficiency is what a heat engine approaches when the two reservoirs are at the same temperature, since η = 1 − T_C/T_H vanishes when T_C equals T_H, but that is a special condition rather than the general statement.  (b) Option (2) is impossible on the definition alone. Efficiency is the ratio of the work obtained to the heat supplied, and by the first law the work obtained cannot exceed the heat supplied, so the ratio cannot exceed one, let alone become infinite. An efficiency greater than one would be a perpetual motion machine of the first kind, creating energy from nothing. Note the contrast with a refrigerator or heat pump, whose coefficient of performance can and routinely does exceed one — but that is a different figure of merit, defined as heat moved per unit of work supplied, and it is not an efficiency.  (c) Option (3) is the serious distractor, because an efficiency of one violates nothing in the first law — energy would still be conserved if a machine turned all the heat it absorbed into work. What forbids it is exactly the second law, in the Kelvin-Planck form: no process can have as its sole result the complete conversion of heat from a single reservoir into work. Such a machine is a perpetual motion machine of the second kind. The whole point of the second law is that it rules out this case and nothing in the first law does, so a candidate who marks 'one' has answered by the first law and ignored the law the question names.

Concept: A heat engine is any device that operates in a cycle, absorbing heat from a hot reservoir, converting some of it into work, and rejecting the rest to a cold reservoir. The second law of thermodynamics constrains what such a device can do, and it has two classical statements that are logically equivalent. The Kelvin-Planck statement, framed for engines, says no process is possible whose sole result is the absorption of heat from a reservoir and its complete conversion into work. The Clausius statement, framed for refrigerators, says no process is possible whose sole result is the transfer of heat from a colder body to a hotter one — heat does not flow uphill by itself. Each can be derived from the other, and both are expressions of a deeper idea captured by entropy: the entropy of an isolated system never decreases, so processes have a direction, and the natural direction is towards greater disorder and the degradation of energy into less useful forms. Carnot's theorem completes the picture by fixing the ceiling: of all engines working between two given reservoirs, a reversible one is the most efficient, all reversible engines between those reservoirs have the same efficiency whatever their working substance, and that efficiency is 1 − T_C/T_H with temperatures on the absolute scale.

State PCS 2026 Q55 — Science & Technology PYQ with Answer

State PCS 2026 Q55 — Science & Technology PYQ with Answer