Question

A 200L tank is evacuated and then filled through a valve connected to an air reservoir at 1 MPa and 20 °C. The valve is shut off when the pressure in the tank reaches 0.5 MPa. What is the mass of air in the tank?

Answer 1

Answer:

The air mass in the tank is 23.78 kg

Solution:

As per the question:

Volume of the tank, $V_{t} = 200 l = 2\times 10^{- 3} m^{3}$

Pressure, P = 1 MPa = $1\times 10^{6} Pa$

Temperature, T = $20^{\circ}C$ = 273 + 20 = 293 K

Pressure, P' = 0.5 MPa = $0.5\times 10^{6} Pa$

Now,

To calculate the air mass, $m_{a}$ we use:

$PV_{t} = m_{a}RT$

where

R = Rydberg constant = 0.287 J/kg.K

$1\times 10^{6}\times 2\times 10^{- 3} = m_{a}0.287\times 293$

$m_{a} = 23.78 kg$