An ideal gas is confined within a closed cylinder at a pressure of 2.026 × 105 Pa by a piston. The piston moves until the volume of the gas

Question

An ideal gas is confined within a closed cylinder at a pressure of 2.026 × 105 Pa by a piston. The piston moves until the volume of the gas is reduced to one-ninth of the initial volume. What is the final pressure of the gas when its temperature returns to its initial value?

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Maya 2 weeks 2021-10-10T19:10:30+00:00 1 Answer 0

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    2021-10-10T19:11:52+00:00

    Answer:

    The final pressure of the gas when its temperature returns to its initial value 1.8234\times 10^6 Pa.

    Step-by-step explanation:

    Given : An ideal gas is confined within a closed cylinder at a pressure of 2.026\times 10^5 Pa by a piston. The piston moves until the volume of the gas is reduced to one-ninth of the initial volume.

    To find : What is the final pressure of the gas when its temperature returns to its initial value?

    Solution :

    Since the temperature is constant
    .

    The relation between P and V is given by,

    P_1\times V_1 = P_2\times V_2

    \frac{P_1}{P_2}=\frac{V_2}{V_1} ….(1)

    The piston moves until the volume of the gas is reduced to one-ninth of the initial volume i.e. V_2=\frac{V_1}{9}

    or \frac{V_2}{V_1}=\frac{1}{9}

    P_1=2.026\times 10^5

    Substitute in equation (1),

    \frac{2.026\times 10^5}{P_2}=\frac{1}{9}

    P_2=9\times 2.026\times 10^5

    P_2=18.234\times 10^5

    P_2=1.8234\times 10^6

    The final pressure of the gas when its temperature returns to its initial value 1.8234\times 10^6 Pa.

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