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A 1 m3 rigid tank initially contains air whose density is 1.18kg/m3. The tank is connected to a high pressure supply line througha valve. The valve is opened, and air is allowed to enter the tankuntil the density in the tank rises to 7.20 kg/m3.

Determine themass of air that has entered the tank.

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cjmejiab

To solve this problem it is necessary to apply the concepts related to density in relation to mass and volume for each of the states presented.

Density can be defined as

[tex]\rho = \frac{m}{V}[/tex]

Where

m = Mass

V = Volume

For state one we know that

[tex]\rho_1 = \frac{m_1}{V}[/tex]

[tex]m_1 = \rho_1 V[/tex]

[tex]m_1 = 1.18*1[/tex]

[tex]m_1 = 1.18Kg[/tex]

For state two we have to

[tex]\rho_2 = \frac{m_2}{V}[/tex]

[tex]m_2 = \rho_2 V[/tex]

[tex]m_1 = 7.2*1[/tex]

[tex]m_1 = 7.2Kg[/tex]

Therefore the total change of mass would be

[tex]\Delta m = m_2-m_1[/tex]

[tex]\Delta m = 7.2-1.18[/tex]

[tex]\Delta m = 6.02Kg[/tex]

Therefore the mass of air that has entered to the tank is 6.02Kg

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