Question

A 2.15-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

Answer: The mass of the air that has entered the tank is 8.858kg

Step-by-step explanation:

Before we can solve to obtain the mass of air that recently gained access into the tank, we must calculate the density of the air that just entered the tank. It is obtained by subtracting the previous density in the tank from the new density in the tank:

= 5.30kg/m^3 - 1.18kg/m^3

= 4.12kg/m^3

So, the density of the air that entered the tank recently is

4.12kg/m^3.

To find the mass of the air, we apply the formula for calculating density and make mass (m), the subject of the formula:

Density = mass/volume

Therefore, mass = Density × volume

The density of the air is 4.12kg/m^3.

The volume of the tank occupied by the air = 2.15m^3

Then, the mass of the air that just entered the tank is:

= 4.12 × 2.15

= 8.858kg

Answer 2

The mass of air that has entered the tank is 8.86Kg

Step-by-step explanation:

We are given:

`Size of tank= 2.15m^3 </p><p>density = 1.18kg/m^3 </p><p> new density = 5.30kg/m^3`

We first calculate the intial and final masses,

Therefore:

`M_initial = p_initial * V`

= 1.18 * 2.15 = 2.54

`M_final = p_final * V`

= 5.30 * 2.15 = 11.4

Therefore to find the mass of air inside the tank, we use:

`ΔM = M_final - M_initial`

= 11.4 - 2.54 = 8.86Kg

Therefore the mass of air inside the tank is 8.86Kg