The speed of sound v in gas might plausibly depend on the pressure p, and the volume V of the gas. Use dimensional analysis to determine the

Question

The speed of sound v in gas might plausibly depend on the pressure p, and the volume V of the gas. Use dimensional analysis to determine the exponents, x,y and z in the Formula. Where C is a dimensionless constant. V=cp^xp^y V^z

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Euphemia 5 years 2021-07-27T14:10:32+00:00 1 Answers 20 views 0

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  1. vankhanh
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    2021-07-27T14:12:08+00:00
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    Answer:

    V= C√p/s

    Explanation:

    We are given that

    Dimension of speed of sound

    V = L T ^-1

    Volume of gas = L³

    Pressure P= M¹L^-1T^-2

    Density =M¹L^-3

    So

    LT^-1 = C [M¹L^-1T^-2]^x [M¹L^-3]^y [L³]^z

    Compare powers

    We have

    x+y=0

    -x+3y+3z=1

    -2x=-1

    So x= 1/2 y= -1/2 z= 0

    So finally we substitute in

    V=cp^xp^y V^z

    We have

    V= C√p/s

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