Question

Which statement is true for the second law of thermodynamics?
(A) Heat can flow spontaneously from a cold object to a hot object
(B) You cannot create a heat engine which extracts heat and converts it all to useful work
(C) According to Planck-Kelvin’s law under some circumstances a perfect heat engine is possible.
(D) None of these

Answer 1

Hint: We know that the second law of thermodynamics states that the total entropy of any isolated system can never decrease over a period of time. The total entropy of an isolated system is constant if and only if all the processes of the system are reversible. According to the second law of thermodynamics, all isolated systems tend to evolve towards thermodynamic equilibrium which is the state with the maximum entropy.

Complete step by step answer:
According to the Kelvin-Planck statement or also known as the heat statement of the second law of thermodynamics, it is impossible to construct or devise an operating heat engine, the sole effect of which is to only absorb energy in the form of heat from a single thermal reservoir and deliver an equal amount of work.
Thus, according to the Kelvin-Planck statement it is impossible to build a heat engine whose efficiency is $100\% $. Or we can also say that, under no circumstances is a perfect heat engine possible.
So, according to the second law of thermodynamics we cannot create a heat engine which extracts and converts it all to useful work. This is because if this state was achieved the engine would be $100\% $efficient. This would ultimately violate the second law of thermodynamics.

Thus, out of all the options given above, we can say that option (B) is accurate.

Note: Even Carnot’s engine is not ideal as for a Carnot’s engine to be $100\% $efficient, either the temperature of the source would have to be infinity or the temperature of the sink would have to be $0K$. Both of which are impossible to achieve.