Write an example in which the first law of thermodynamics is allowed but is never observed.

(N/A) An example of this is given below.
Nobody has ever seen a book lying on a table jumping to a height by itself. Such a phenomenon would be consistent with the first law of thermodynamics (principle of conservation of energy) because the table could cool spontaneously,converting some of its internal energy into an equal amount of mechanical energy for the book,which would then hop to a height with potential energy equal to the mechanical energy it acquired. However,this never happens in reality.
This implies that there is another principle that disallows many phenomena consistent with the first law of thermodynamics,which is known as the second law of thermodynamics.
The second law of thermodynamics provides a fundamental limitation to the efficiency of a heat engine and the coefficient of performance of a refrigerator.
$1$. For a heat engine,the efficiency $\eta = 1 - \frac{Q_2}{Q_1}$ can never be unity (i.e.,$100 \%$),because the heat released $Q_2$ to the cold reservoir (sink) can never be zero. This means the absorbed heat $Q_1$ cannot be converted completely into work.
$2$. For a refrigerator,the second law states that the coefficient of performance $\alpha = \frac{Q_2}{W}$ can never be infinite. Since external work $W$ can never be zero,$\alpha$ remains finite.
Based on these observations,Kelvin-Planck and Clausius formulated statements for the second law of thermodynamics:
$(i)$ Kelvin-Planck Statement: No process is possible whose sole result is the absorption of heat from a reservoir and the complete conversion of the heat into work.
$(ii)$ Clausius Statement: No process is possible whose sole result is the transfer of heat from a colder object to a hotter object.