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2 September, 19:30

The volume of an ideal gas is held constant. Determine the ratio P2/P1 of the final pressure to the initial pressure when the temperature of the gas rises (a) from 48 to 96 K and (b) from 26.0 to 68.7 oC.

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  1. 2 September, 19:38
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    A. 2

    B. 1.14

    Explanation:

    A. Data obtained from the question include:

    Initial temperature (T1) = 48K

    Final temperature (T2) = 96K

    Final pressure (P2) / initial pressure (P1) = ?

    Since the volume is constant, we shall determine the ratio of final pressure to initial pressure (P2/P1) by applying the following equation:

    P1/T1 = P2/T2

    P1/48 = P2 / 96

    Cross multiply

    48 x P2 = P1 x 96

    Divide both side by 48

    P2 = P1 x 96/48

    Divide both side P1

    P2/P1 = 96/48

    P2/P1 = 2

    Therefore, the ratio of final pressure to the initial pressure is 2

    B. Data obtained from the question include:

    Initial temperature (T1) = 26°C = 26°C + 273 = 299K

    Final temperature (T2) = 68.7°C = 68.7°C + 273 = 341.7K

    Final pressure (P2) / initial pressure (P1) = ?

    Since the volume is constant, we shall determine the ratio of final pressure to initial pressure (P2/P1) by applying the following equation:

    P1/T1 = P2/T2

    P1/299 = P2 / 341.7

    Cross multiply

    299 x P2 = P1 x 341.7

    Divide both side by 299

    P2 = P1 x 341.7/299

    Divide both side P1

    P2/P1 = 341.7/299

    P2/P1 = 1.14

    Therefore, the ratio of final pressure to the initial pressure is 1.14
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