In the equation X + a Y 2 [ Y - b ] = R T ,   X is pressure, Y is volume, R is universal gas constant…

In the equation X+aY2[Y-b]=RT, X is pressure, Y is volume, R is universal gas constant and T is temperature. The physical quantity equivalent to the ratio ab is:

 

  1. Pressure gradient
  2. Energy
  3. Impulse
  4. Coefficient of viscosity

Solution

$X$ and $\frac{a}{Y^2}$ have the same dimensions. $Y$ and $b$ also have the same dimensions. Therefore, $\begin{aligned} \frac{a}{Y^2} &= M L^{-1} T^{-2} \\ \Rightarrow a &= M L^{-1} T^{-2} \times L^6 = M L^5 T^{-2} \end{aligned}$ and $b = L^3$. So, the dimensions of $\frac{a}{b}$ is, $\begin{aligned} \frac{a}{b} &= \frac{M L^5 T^{-2}}{L^3} = M L^2 T^{-2} \end{aligned}$ This is the dimensional form of energy. Hence, this is the right option.

Asked in: JEE Main 2023 (13 Apr Shift 2)

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