An expansion vessel is added to a heating system to avoid the overpressure forming in the system due to the expansion of water. The vessel consists of a cylinder of volume V, that is divided into two parts by a freely moving thin partition. One of these parts is filled with compressed air (T0=\SI20\degreeCelsius) to a pressure p0, taking under it all of the cylinder’s volume. Next, the other part of the cylinder is connected to the heating system at a temperature T1=T0 and the system is filled with water until a pressure p1=\SI300kPa is reached and the total volume of the water in the system is Vs=\SI100L. After this β=10% of the expansion vessel is filled with water. In winter the volume of the water in the system increases by α=\SI1% due to the heating and in result the pressure of the system increases to p2, moreover the air in the expansion vessel is warmed to a temperature T2=\SI40\degreeCelsius. Find how big must be the initial air pressure p0 in the expansion vessel and the minimal volume of the vessel V, so that the extra pressure Δp=p2−p1 formed in result of the water’s expansion would not be bigger than 50 kPa.