A tank has two rooms separated by a membrane Room A has 1kgo

A tank has two rooms separated by a membrane. Room A has 1kgof air and a volume of 0.5m³, room B has 0.75m³ of air with a density 0.8 kg/m³. Themembrane is broken and the air comes to a uniform state. Find thefinal density of the air

Solution

{Volume Of RoomA} = V_A = 0.5 m^3
{Air Mass In Room A} = M_A = 1.0kg

{Volume Of Room B} = V_B = 0.75m^3
{Density Of Air In Room B} = D_B = 0.8 kg/m^3
{Air Mass In Room B} = M_B = (V_B)*(D_B) =
          = (0.75)*(0.8)
          = 0.6kg

{Combined Air Mass, Rooms A & B} = M =
          = (1.0kg) + (0.6 kg)
          = 1.6kg
{Combined Volume, Rooms A & B} = V =
          = (0.5m^3) + (0.75 m^3)
          = 1.25m^3

{Final Air Density} = D = M/V =
          = (1.6 kg)/(1.25m^3)
          = 1.28 kg/m^3