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14 March, 10:45

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?

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  1. 14 March, 12:15
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    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
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