Problem 11.010 IS A rigid tank contains 1 kg of oxygen (O2) at p1 = 30 bar, T1 = 180 K. The gas is cooled until the temperature drops to 150 K. Determine the volume of the tank, in m3, and the final pressure, in bar, using the:

The gas law relation is

PV = nRT where n is no of moles of gas

given 1 kg of oxygen

n = 1000 / 32 = 31.25 moles

P = 30 bar = 30 x 10⁵ Pa

V = ?

T = 180 K

R = 8.32

Substituting the values

30 x 10⁵ x V = 31.25 x 8.32 x 180

V = 1560 x 10⁻⁵ m³

= 1.56 x 10⁻² m³

When volume remains constant, pressure is proportional to temperature

P₂ / P₁ = T₂ / T₁

P₂ = (150 / 180) x 30

= 25 Bar.