The (kelvin-planck statement of the) second law of thermodynamics reads as follows: it is impossible for an engine working in a cycle to produce no other effect than that of extracting heat from a reservoir and performing an equivalent amount of work. the phrase "in a cycle" does not apply in this situation, so the second law does not forbid heat being converted entirely into work. for this particular problem, is all of the heat energy absorbed by the gas in fact turned into work done on the piston

For this particular problem, it is possible that all the thermal energy absorbed by the gas becomes work done by the piston.

Explanation:

It is important to note that the Kelvin-Planck statement refers to cyclic processes, which leave the system in a final state equal to the initial one. It is possible to transform calories at work if the final state is different from the initial state. An example of this is in an isothermal expansion of a gas, all the heat that enters is transformed entirely in the work, but in the end the volume of the gas is different from the initial one.

wavelength divides in half and speed stays the same.