Define Teacup Engine?

The astronaut was calmly drinking tea at five o'clock galactic time, as was his wont, when he had an urgent situation outside the shuttle and he had to do an EVA to deal with it.  In the lead to leaving the ship his jetpack failed and nothing remained to connect him to the shuttle. Auspiciously, he had forgetfully brought his teacup with him. Ever since this was the only cup he had, he didn't want to throw it away in order to propel him back to the shuttle besides, it was his favorite cup. In its place, he used the sublimation of the frozen tea to propel him back to the spaceship. Was it really possible?  Guess the time it might take him to return if he is a distance L=40 m from the ship. Presume that the sublimation take place at a constant temperature T=273K.

The vapor pressure by this temperature is P₀=600P_a, and the total mass of the astronaut M=110 kg.