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30 January, 18:51

A certain flexible weather balloon contains helium gas at a volume of 855 L. Initially, the balloon is at sea level where the temperature is 25°C and the barometric pressure is 728 torr. The balloon then rises to an altitude of 6000 ft, where the pressure is 605 torr and the temperature is 15°C. What is the change in volume of the balloon (in L) as it ascends from sea level to 6000 ft?

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  1. 30 January, 18:53
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    The volume at 6000 ft is 994.3 L.

    The change in volume is 139.3 L

    Explanation:

    Step 1: Data given

    Volume of the gas = 855L

    Temperature = 25.0 °C = 273 + 25 = 298 Kelvin

    barometric pressure = 728 torr

    When the balloon rises 6000 ft, the pressure is 605 torr

    temperature = 15.0°C = 273 + 15 = 288 Kelvin

    Step 2: Calculate the new volume

    (p1*V1) / T1 = (P2*V2) / T2

    ⇒ with P1 = the initial pressure of gas in the balloon = 728 torr

    ⇒ with V1 = the initial volume = 855 L

    ⇒ with T1 = the initial temperature = 298 Kelvin

    ⇒ with P2 = the pressure after rising to 6000 ft = 605 torr

    ⇒ with V2 = the volume of the gas at 6000 ft

    ⇒ with T2 = the temperature at 6000 ft = 288 Kelvin

    V2 = (P1 * T2 * V1) / (P2*T1)

    V2 = (728*288*855) / (605*298)

    V2 = 994.3 L

    The change in volume = 994.3 - 855 = 139.3 L

    The volume at 6000 ft is 994.3 L.

    The change in volume is 139.3 L
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