Is this a spontaneous or a non-spontaneous process?

An insulated tank initially contains a liquid-vapor mixture of water. Then, an electric heater is turned on and kept inside the tank until all the liquid becomes saturated vapor.

According to the 2nd Law of Thermodynamics, a spontaneous process occurs when the change in entropy of the universe is greater than zero.

In this case, since the tank is insulated, $Q=0$ and the change in entropy of the surroundings is also equal to $0$; hence, $\Delta S_\mathrm{universe}$ = $\Delta S_\mathrm{system}$. Since adding work to the system (via the electric heater) results in an increase of the thermal energy of water and its evaporation, $\Delta S_\mathrm{system}>0$. Therefore, $\Delta S_\mathrm{universe} > 0$, and the process is spontaneous.

But wouldn't the necessity of adding work to the system (in order for the water to evaporate) mean the process is non-spontaneous?

• Two questions. Does it take energy to run the heater? If so, where did the energy to run the heater come from, inside the tank or outside the tank?
– MaxW
Dec 1 '17 at 16:05