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
Step 1: Understand the Principle of Homogeneity. The Principle of Homogeneity states that for an equation to be dimensionally consistent, all terms added or subtracted must have the same dimensions. In the given van der Waals equation: (P + (a)/(V^2))(V - b) = RT For the term (P + (a)/(V^2)), the dimensions of P must be the same as the dimensions of (a)/(V^2). Therefore, we can write: The base units of P = The base units of (a)/(V^2) Step 2: Express the relationship to find the base units of a. From the equality above, we can rearrange to solve for the base units of a: The base units of a = (The base units of P) × (The base units of V)^2 Step 3: Determine the base units for Pressure (P) and Volume (V). • Pressure (P) is defined as Force per unit Area. Force (F) has base units of kg · m · s^-2 (from F=ma). Area (A) has base units of m^2. So, the base units of P = kg · m · s^-2m^2 = kg · m^-1 · s^-2. • Volume (V) has base units of m^3. Step 4: Substitute the base units into the expression for a. The base units of a = (kg · m^-1 · s^-2) × (m^3)^2 The base units of a = kg · m^-1 · s^-2 × m^6 Combine the powers of m: The base units of a = kg · m^(-1+6) · s^-2 The base units of a = kg · m^5 · s^-2 The final answer is kg · m^5 · s^-2.