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12 April, 15:44

A helium-filled balloon has a volume of 1.6 m3. As it rises in the Earth's atmosphere, its volume changes. What is its new volume if its original temperature and pressure are 16◦C and 1.3 atm and its final temperature and pressure are - 41◦C and 1.2 atm? Answer in units of m

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  1. 12 April, 18:28
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    Answer: 1.39 m3

    Explanation:

    If we consider the helium to be an ideal gas, at any condition, we can apply the Ideal Gas Equation as follows:

    P V = n R T

    Taking the initial state as (1), we can write:

    P1V1 = n R T1 (1)

    In the initial state, we have P = 1.3 atm, V=1.6 m3, and T = 273 K + 16 K = 289 K.

    Let's call (2) to the final state, so we can write as follows:

    P2V2 = n R T2 (2)

    In the final state, our givens are P = 1.2 atm, and T = 273 K - 41 K = 232 K

    So, dividing both sides in (1) and (2), we can solve for V2, as follows:

    V2 = (1.3 atm. 1.6 m3.232 K) / 1.2 atm. 289 K = 1.39 m3
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