Question

A 2-m3 rigid tank initially contains air whose density is 1.18 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 5.30 kg/m3 . Determine the mass of air that has entered the tank?

Answer 1

Explanation:

It is known that density is the mass present in per unit volume.

Mathematically,         Density = $\frac{mass}{volume}$

Since, it is given that $d_{1}$ is 1.18 $kg/m^{3}$, $d_{2}$ is 5.30 $kg/m^{3}$, and volume is 2 $m^{3}$.

Therefore, mass of air that has entered will be $m_{2}$ -  $m_{1}$ and it will be calculated as follows.

                       $d_{2} - d_{1}$ = $\frac{m_{2} - m_{1}}{Volume}$

      $m_{2} - m_{1}$ = $(5.30 kg/m^{3} - 1.18 kg/m^{3}) \times 2 m^{3}$

                                            = 8.24 kg

Thus, we can conclude that mass of air that has entered the tank is 8.24 kg.