Give the units of Vander Waal’s constants a and b.
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The Van der Waals equation of state is
(P + a/V^2) (V - b) = RT
Where P is pressure, V is volume and T is temperature.
The dimensions of
[P] = [F/A] = [MLT^ −2/L^2] = [ML^−1T^ −2]
[V] = [L^3]
We cannot add or subtract quantities of different dimensions.
Therefore
[P] = [a/V^2]
[a] = [PV^2] = [ML^−1T ^−2 L^6]
= [M L^5 T ^−2]
Therefore [a] = [M L^5 T^ −2]
Similarly,
[b] = [V] = [L^3]
(P + a/V^2) (V - b) = RT
Where P is pressure, V is volume and T is temperature.
The dimensions of
[P] = [F/A] = [MLT^ −2/L^2] = [ML^−1T^ −2]
[V] = [L^3]
We cannot add or subtract quantities of different dimensions.
Therefore
[P] = [a/V^2]
[a] = [PV^2] = [ML^−1T ^−2 L^6]
= [M L^5 T ^−2]
Therefore [a] = [M L^5 T^ −2]
Similarly,
[b] = [V] = [L^3]
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