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

The air mass in the tank is 23.78 kg

Solution:

As per the question:

Volume of the tank,
`V_(t) = 200 l = 2* 10^(- 3) m^(3)`

Pressure, P = 1 MPa =
`1* 10^(6) Pa`

Temperature, T =
`20^(\circ)C` = 273 + 20 = 293 K

Pressure, P' = 0.5 MPa =
`0.5* 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* 10^(6)* 2* 10^(- 3) = m_(a)0.287* 293`

`m_(a) = 23.78 kg`