Question is obvious: Why can't we make Carnot heat engine in real life? I read Wikipedia and Fundamentals of Physics (Halliday) but I didn't found anything about my question. there we're explanations about formulas and how it work but no obvious answer why it can't be made.
A Carnot engine has to be perfectly reversible. This means zero friction, and perfect thermal conductivity between reservoirs*.
In practice neither of these things are possible so you will only ever get "close".
* As was pointed out by David White, reversibility requires zero temperature difference between the reservoirs; since the flow of heat is proportional to thermal gradient, an infinitesimal temperature difference implies infinitesimal heat flow, and infinite time per cycle; this is one more reason why the perfect heat engine is thermodynamically out of reach
As Floris points out the Carnot engine has to be perfectly reversible.
So, for example, the isothermal expansion step requires the resistance to the expansion of the gas to be always just a little bit less than the pressure of the gas inside the cylinder or engine. The pressure drops during the expansion and so the force pushing back on the gas must drop in exactly the same way. If the force pushing back on the gas is higher than this then gas will be compressed. If the pressure is significantly lower then the gas will expand rapidly and its temperature will drop.
Similarly the force compressing the gas in the isothermal compression would have to be just enough to slowly compress the gas - and slowly increase with time.
In a real engine the resistance to motion (= pressure exerted on gas) cannot be controlled in this way and so the Carnot cycle cannot be reproduced in a real engine.
Irreversibility cannot be the answer because after all, NO engines AT ALL can use absolutely reversible procedures: there are no reversible procedures in nature. So not even the Otto machine can really exist.
I think the answer lies in the impossible adiabatic changes (producing Work by only changing the temperature of the gas, cooling it, with no heat exchange) but I am not sure.
As what they said above, carnot engine has to be perfectly reversible. We know the second law of thermodynamics, "The entropy of an isolated subject always increases." But Qapplied = T1*(s4-s1) and Qrejection = T2*(s2-s3) has constant change of entropy, this then violates the second law.
Edit: If are asking why people need to study carnot engine (impossible), it's because it serves as a basic background of all the engines.