In the equation , X is pressure, Y is volume, R is universal gas constant and T is temperature. The physical quantity a equivalent to the ratio is [2023]

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Solution

Q.
In the equation $[X + \frac{a}{Y^{2}}] [Y - b] = R T$ , X is pressure, Y is volume, R is universal gas constant and T is temperature. The physical quantity a equivalent to the ratio $\frac{a}{b}$ is [2023]

1 Energy

2 Impulse

3 Pressure gradient

4 Coefficient of viscosity

Ans.
(1)

X and $\frac{a}{Y^{2}}$ have same dimensions

Y and b have same dimensions

$∴ [a] = [M L^{5} T^{- 2}]$

$[b] = [L^{3}]$

$\frac{[a]}{[b]} = [M L^{2} T^{- 2}]$ has dimensions of energy.

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