Answered

A 3.5-m3 rigid tank initially contains air whose density is 2 kg/m3 . The tank is connected to a high-pressure supply line through a valve. The valve is opened, and air is allowed to enter the tank until the density in the tank rises to 6.5 kg/m3 . Determine the mass of air that has entered the tank.

Answer :

Answer:

Explanation:

First, we find the mass of the air originally in the tank.

Density is given as mass divided by volume. It is given as:

[tex]Density = \frac{mass}{volume}[/tex]

Therefore, mass is:

[tex]mass = denisty *volume[/tex]

Density of air = [tex]2 kg/m^3[/tex]; Volume of the tank =  [tex]3.5 m^3[/tex]

[tex]=> Mass = 3.5 * 2 = 7 kg[/tex]

The mass of the air initially in the tank is 7 kg.

After air is allowed to enter, the mass changes.

New density = [tex]6.5 kg/m^3[/tex]

The new mass will be:

[tex]Mass = 6.5 * 3.5 = 22.75 kg[/tex]

We can now find the mass of air that has entered the tank:

Mass of air that entered tank = New mass of air - Original mass of air

M = 22.75 - 7.0 = 15.75 kg

The mass of air that entered the tank is 15.75 kg.

Other Questions