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24 March, 20:23

Consider a sample of gas in a container on a comfortable spring day in chicago, il. the celsius temperature suddenly doubles, and you transfer the gas to a container with twice the volume of the first container. if the original pressure was 12 atm, what is a good estimate for the new pressure?

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  1. 24 March, 22:52
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    To solve this problem, we must first assume that the gas acts like an ideal gas so that we can use the ideal gas equation:

    P V = n R T

    where P is the pressure, V is the volume, n is the number of moles, R is the universal gas constant and T is the absolute temperature

    Assuming that the number of moles is constant, then we can write all the variables in the left side:

    P V / T = k where k is a constant (n times R)

    Equating two conditions or two states:

    P1 V1 / T1 = P2 V2 / T2

    We are given that V2 = 2 V1 therefore

    P1 V1 T2 = P2 (2V1) T1

    P1 T2 = 2 P2 T1

    Additionally we are given that the temperature in Celsius is doubled, however in the formula we use the absolute temperature in Kelvin, therefore:

    T1 (K) = T1 + 273.15

    T2 (K) = 2T1 + 273.15

    and P1 = 12 atm

    Substituting:

    12 (2T1 + 273.15) = 2 P2 (T1 + 273.15)

    P2 = 6 (2T1 + 273.15) / (T1 + 273.15)

    Assuming that a nice spring day in Chicago has a temperature of 15 Celsius, therefore:

    P2 = 6 (2*15 + 273.15) / (15 + 273.15)

    P2 = 6.312 atm
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