Question

A compressed air tank contains 4.6 kg of air at a temperature of 77 °C. A gage on the tank reads 300 kPa. Determine the volume of the tank.

Answer 1

Answer : The volume of the tank is, 1.54 mL

Explanation :

To calculate the volume of gas we are using ideal gas equation:

`PV=nRT\\\\PV=(w)/(M)RT`

where,

P = pressure of gas = 300 kPa = 2.96 atm

Conversion used : (1 atm = 101.325 kPa)

V = volume of gas = ?

T = temperature of gas =
`77^oC=273+77=350K`

R = gas constant = 0.0821 L.atm/mole.K

w = mass of gas = 4.6 kg = 4600 g

M = molar mass of air = 28.96 g/mole

Now put all the given values in the ideal gas equation, we get:

`(2.96atm)* V=(4600g)/(28.96g/mole)* (0.0821L.atm/mole.K)* (350K)`

`V=1541.98L=1.54mL` (1 L = 1000 mL)

Therefore, the volume of the tank is, 1.54 mL