This physics problem tests your understanding of fundamental physical laws and their applications. The step-by-step solution below breaks down the problem using relevant equations and physical reasoning.
ScanSolve AI Answer
To check the dimensional consistency of the equation J = D × A × ( L)/( x), we need to determine the dimensions of each term. Step 1: Identify the dimensions of each variable. J (Drug diffusion rate): Mass of drugs crossing membrane per second. [J] = [M T^-1] A (Area): Length squared. [A] = [L^2] ( L)/( x) (Concentration gradient): Concentration ( L) is typically mass per unit volume. [Concentration] = [M L^-3] x is a change in position, so it has dimensions of length. [ x] = [L] Therefore, the dimensions of the concentration gradient are: [( L)/( x)] = [M L^-3][L] = [M L^-4] D (Diffusion coefficient, denoted as in the image): The standard dimensions for a diffusion coefficient are length squared per unit time. [D] = [L^2 T^-1] Step 2: Substitute the dimensions into the given equation. The equation is J = D × A × ( L)/( x). We will compare the dimensions of the Left Hand Side (LHS) with the dimensions of the Right Hand Side (RHS). LHS dimensions: [J] = [M T^-1] RHS dimensions: [D] × [A] × [( L)/( x)] Substitute the dimensions found in Step 1: [L^2 T^-1] × [L^2] × [M L^-4] Combine the terms: [M · L^2+2-4 · T^-1] [M · L^0 · T^-1] [M T^-1] Step 3: Compare the dimensions of the LHS and RHS. The dimensions of the LHS are [M T^-1]. The dimensions of the RHS are [M T^-1]. Since the dimensions on both sides of the equation match, the equation is dimensionally consistent. The equation is dimensionally consistent. That's 2 down. 3 left today — send the next one.