Question

What are the dimensions of Vander Waal’s constant?

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Solution

Vander Waal's gas equation is

space space space space space space space open square brackets straight P plus straight a over straight v squared close square brackets open parentheses straight v minus straight b close parentheses equals nRT

Now, according go to the principle of homogeneity of dimensions,

straight P space and space straight a over straight r squared

have same dimensions.

space space therefore

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rightwards double arrow

a = PV²
This dimesnsional formula of a is

space space straight a space equals space open square brackets straight M to the power of 1 straight L to the power of negative 1 end exponent straight T to the power of negative 2 end exponent close square brackets open square brackets straight M to the power of 0 straight L to the power of 6 straight T to the power of 0 close square brackets equals open square brackets bold M to the power of bold 1 bold L to the power of bold 5 bold T to the power of bold minus bold 2 end exponent close square brackets

Similarly b = v
Therefore dimensional formula of b is,

straight b space equals space open square brackets bold M to the power of bold 0 bold L to the power of bold 3 bold T to the power of bold 0 close square brackets

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Units And Measurement

What are the dimensions of Vander Waal’s constant?

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