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The equation given below is the Vandar W...

The equation given below is the Vandar Wall's equation for a gas `(P+(a)/(V^2))(V-b)=RT`
where P is the pressure, V is the volume, R is the universal gas constant and T is the temperature. Find the dimensions of `a"/"b`.

Text Solution

Verified by Experts

`[P]=((a)/(V^2))` (only quantities of similar dimension can be added or subtracted)
`[a]=[PV^(2)]`
`[ML^(-1)T^(-2)][L^3]^(2)= [ML^(5)T^(-2)]`
Similar, `[b]=[V]=[L^3]`
`[(a)/(b)]=[(ML^(5)T^(-2))/(L^(3))]=[ML^(2)T^(-2)]`.
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Knowledge Check

  • The van der Waals equation for 1 mole of gas is (p+a/V^(2))(V-b)=RT where,

    A
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    C
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    `[ML^(5)T^(-2)]`
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    `[ML^(-1)T^(-2)]`
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    `[L^(3)]`
    D
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    A
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    B
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    C
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    D
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