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1st Law of Thermodynamics

What is the u...

Question

What is the unit of " $a$ " in Vander Waal's gas equation?

A t m \times l i t r e^{- 2} m o l^{2}

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A t m \times l i t r e^{- 2}

/ mol

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A t m \times l i t r e^{- 1} m o l^{2}

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A t m \times l i t r e^{2} m o l^{- 2}

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Solution

The correct option is D $A t m \times l i t r e^{2} m o l^{- 2}$
Van der Waals gas equation is given by
$(P + \frac{a n^{2}}{V^{2}}) (V - n b) = n R T$
For the equation to be dimensionally consistent, $\frac{a n^{2}}{V^{2}}$ should have the dimension of pressure.
$\frac{a n^{2}}{V^{2}} = A t m$
$a = A t m . \frac{l i t^{2}}{m o l^{2}} = A t m . l i t^{2} . m o l e^{- 2}$

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