On this page
Students often learn the two statements of the second law as two sentences to memorise, then freeze when a question asks whether a fridge, heat pump or engine is possible. This post explains what each statement forbids, shows with numbers why they are the same law, and gives a routine for "is this device possible?" questions.
Where is the second law in the syllabus?
NCERT Class 11 Chapter 11, Thermodynamics, section 11.9, gives both statements. Kelvin-Planck: "No process is possible whose sole result is the absorption of heat from a reservoir and the complete conversion of the heat into work." Clausius: "No process is possible whose sole result is the transfer of heat from a colder object to a hotter object." The chapter adds that the two are completely equivalent. The CBSE Physics curriculum for 2026-27 lists the second law in the same chapter, and the JEE (Main) 2026 syllabus lists "The second law of thermodynamics: reversible and irreversible processes". Check the syllabus for your exam year.
What does each statement actually forbid?
The key words are "sole result". A car engine turns heat into work, but it also dumps heat into the air, so it is allowed. A refrigerator moves heat from its cold inside to the warmer kitchen, but only because the compressor does work on it, so it is allowed too. What is forbidden is a perfect engine (all heat into work, nothing rejected) or a perfect refrigerator (heat flows uphill with no work done).
NCERT puts it in performance terms: an engine's efficiency can never be 1, and a refrigerator's coefficient of performance can never be infinite.
Worked example 1: is this freezer claim possible?
A freezer keeps its inside at −18 °C in a 30 °C kitchen. A seller claims it removes 800 J from the inside for every 100 J of electrical work, a coefficient of performance of 8.
For a refrigerator, the coefficient of performance is α = Q2/W, where Q2 is the heat taken from the cold side. For an ideal reversible refrigerator, Q1/Q2 = T1/T2, which gives the limit α = T2/(T1 − T2) in kelvin.
T2 = 273 − 18 = 255 K, T1 = 273 + 30 = 303 K.
α(max) = 255/(303 − 255) = 255/48 ≈ 5.3.
A claimed 8 is above the limit, so the claim breaks the second law. A claim of 3 would be possible: the freezer would take 300 J from inside, use 100 J of work and release 400 J into the kitchen.
Why are the two statements the same law?
You show equivalence by proving that breaking one statement lets you break the other.
Worked example 2: a perfect refrigerator breaks Kelvin-Planck. Take an ordinary engine that takes 1000 J from the hot reservoir, does 400 J of work and rejects 600 J to the cold reservoir. Now add a "perfect" refrigerator that moves 600 J from cold back to hot with no work. Combined, the cold reservoir gains and loses 600 J, so it is unchanged. The hot reservoir loses 1000 − 600 = 400 J, and 400 J of work comes out. The sole result is heat from one reservoir turned completely into work, which Kelvin-Planck forbids.
Worked example 3: a perfect engine breaks Clausius. Take a "perfect" engine that turns 200 J from the hot reservoir into 200 J of work. Use that work to run an ordinary refrigerator with α = 3: it takes 600 J from the cold side and delivers 800 J to the hot side. Net: the cold side loses 600 J, the hot side gains 800 − 200 = 600 J, and no outside work is used. The sole result is 600 J moving from cold to hot, which Clausius forbids.
Why do students find this hard?
In a study of an introductory calculus-based course, Christensen, Meltzer and Ogilvie (2009) found that no more than 6% of students gave fully correct answers on entropy questions before instruction, and nearly two-thirds reasoned as if entropy were conserved, with little change after standard teaching. In upper-division courses, Smith and colleagues (2015) found that students struggled to reason about situations that are physically impossible and did not clearly connect the Carnot cycle to the second law. "Is this device possible?" is exactly that kind of reasoning, so practise it on purpose.
Which mistakes cost marks?
Saying a fridge breaks the second law. It does not, because work is done on it. Point to the "sole result" wording.
Treating the second law as energy conservation. A perfect engine conserves energy and is still forbidden.
Using Celsius in COP or efficiency limits. Always convert first.
Mixing up Q1 and Q2. In a refrigerator, α = Q2/W uses the heat taken from the cold side; the heat released to the room is Q2 + W.
A practice routine
Write both statements from memory, underlining "sole result".
Do three device-claim questions: compute the limit first, then compare.
Redo examples 2 and 3 with your own numbers until you can draw the combined device without notes.
Read our worked heat engine and Carnot efficiency problems for the engine side, and the story of Rudolf Clausius for where the idea came from.
If the combined-device argument still feels slippery, the Fermi Problem Library has worked problems with a step-by-step solver that explains the reasoning rather than printing an answer.
Tonight, take one engine or fridge question from your textbook and decide whether it is possible before you calculate anything else.
