A small research submarine with a volume of 1.2 x 105 L has an internal pressure of 1.0 atm and an internal temperature of 150 C. If the submarine descends to a depth where the pressure is 150 atm and the temperature is 30 C, what will the volume of the gas inside be if the hull of the submarine breaks?

V₂ = 570 L

Explanation:

Given dа ta:

Initial volume = 1.2 * 10⁵ L

Initial pressure = 1 atm

Initial temperature = 150 °C (150 + 273 = 423 K)

Final temperature = 30°C (30+273 = 303 K)

Final volume = ?

Final pressure = 150 atm

Formula:

P₁V₁/T₁ = P₂V₂/T₂

P₁ = Initial pressure

V₁ = Initial volume

T₁ = Initial temperature

P₂ = Final pressure

V₂ = Final volume

T₂ = Final temperature

Solution:

V₂ = P₁V₁ T₂ / T₁ P₂

V₂ = 1.0 atm * 1.2 * 10⁵ L * 303 K / 423 K * 150 atm

V₂ = 363.6*10⁵ L atm. L. K / 63450 K. atm

V₂ = 0.0057*10⁵ L

V₂ = 570 L