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7 May, 22:42

What is the increase in pressure required to decrease volume of mercury by 0.001%

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  1. 7 May, 22:54
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    Using Boyles law

    Boyle's law states that, the volume of a given gas is inversely proportional to it's pressure, provided that temperature is constant

    V ∝ 1 / P

    V = k / P

    VP = k

    Then,

    V_1 • P_1 = V_2 • P_2

    So, if we want an increase in pressure that will decrease volume of mercury by 0.001%

    Then, let initial volume be V_1 = V

    New volume is V_2 = 0.001% of V

    V_2 = 0.00001•V

    Let initial pressure be P_1 = P

    So,

    Using the equation above

    V_1•P_1 = V_2•P_2

    V * P = 0.00001•V * P_2

    Make P_2 subject of formula by dividing be 0.00001•V

    P_2 = V * P / 0.00001 * V

    Then,

    P_2 = 100000 P

    So, the new pressure has to be 10^5 times of the old pressure

    Now, using bulk modulus

    Bulk modulus of mercury=2.8x10¹⁰N/m²

    bulk modulus = P / (-∆V/V)

    -∆V = 0.001% of V

    -∆V = 0.00001•V

    -∆V = 10^-5•V

    -∆V/V = 10^-5

    Them,

    Bulk modulus = P / (-∆V/V)

    2.8 * 10^10 = P / 10^-5

    P = 2.8 * 10^10 * 10^-5

    P = 2.8 * 10^5 N/m²
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