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in van der waals equation unit and dimension {p + a \v²} {v - b} =RT obtain the dimension of the constant a and b, where p is pressure, v is volume, T is temperature and R is gas constant​

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Final answer:

In the Van der Waals equation, the dimension of the constant a is M L^5 T^-2, and for constant b, it is L^3, which corresponds to adjustments for molecular attractions and molecular size, respectively.

Step-by-step explanation:

The student's question is about determining the dimension of constants a and b in the Van der Waals equation of state. This equation accounts for the non-ideal behavior of gases by incorporating these constants, which account for molecular attractions (constant a) and molecular size (constant b). Using the Van der Waals equation, (p + a/v²)(v - b) = RT, where p is the pressure, v is the volume, R is the gas constant, and T is the temperature, we can derive the dimensions of a and b.

To determine the dimension of constant a, we look at the term a/v², which adds to pressure. Since pressure (p) has the dimension of (M L⁻¹ T⁻²), and it is added to a/v², the dimensions of a must be such that a/v² will also have the dimension of pressure. So, the dimension for a is obtained as M L⁵ T⁻².

For constant b, the term v - b is in volume units. Since the constant b is subtracted from v (which has dimension L³), the dimension for b is simply L³.

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