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1 May, 05:18

A plastic bottle is closed outdoors on a cold day when the temperature is - 15.0°C and is later brought inside where the temperature is 21.5°C. What is the pressure of the air in the bottle after it reaches room temperature, assuming the air in the bottle was at a pressure of 1.00 atm upon reaching thermal equilibrium with the outdoor temperature?

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  1. 1 May, 05:43
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    Pressure = 1.14 atm

    Explanation:

    Hello,

    This question requires us to calculate the final pressure of the bottle after thermal equilibrium.

    This is a direct application of pressure law which states that in a fixed mass of gas, the pressure of a given gas is directly proportional to its temperature, provided that volume remains constant.

    Mathematically, what this implies is

    P = kT k = P / T

    P1 / T1 = P2 / T2 = P3 / T3 = ... = Pn / Tn

    P1 / T1 = P2 / T2

    P1 = 1.0atm

    T1 = - 15°C = (-15 + 273.15) K = 258.15K

    P2 = ?

    T2 = 21.5°C = (21.5 + 273.15) K = 294.65K

    P1 / T1 = P2 / T2

    P2 = (P1 * T2) / T1

    P2 = (1.0 * 294.65) / 258.15

    P2 = 1.14atm

    The pressure of the gas after attaining equilibrium is 1.14atm
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