In this paper a proposed apparatus for seawater desalination at low temperature and low pressure is discussed. Based on the idea of Torricelli barometer, water vapor above seawater and water vapor above fresh water are forced to gather in a tube connecting the two water sources in nearly vacuum environment. Creating temperature difference between the two water sources develops large pressure difference between the saturated water vapor pressures above the two water sources. This pressure difference forces water vapor to move from the hotter seawater surface to condense in the cooler fresh water area. The apparatus automatically substitutes the evaporated seawater and transmits the fresh water to where it is needed, i.e. no energy is required to feed the apparatus with seawater or to transfer fresh water. The apparatus also automatically get rid of brine (more salty seawater due to evaporation) by replacing with fresh warm seawater. The variability of atmospheric surface pressure due to season change or the passage of atmospheric systems that can disturb the apparatus performance is also considered. The study indicates, theoretically, that this technique which was known to be suitable for small-scale freshwater needs can yield one order of magnitude larger than expected. Theoretically, it is shown that with the simple proposed apparatus, the estimated fresh water yield can be more than 10 m3 per day. Experiments are required to test the idea.