Final answer:
The units of the constant 26 in the mean free path formula L = 26 * W * V * R * T are 1/(m² * s²). This ensures that the mean free path L, expressed in meters, has consistent units throughout the formula.
Step-by-step explanation:
To determine the units of the constant 26 in the formula L = 26 * W * V * R * T for estimating the mean free path of a perfect gas, we need to ensure that the units on both sides of the equation match. The mean free path L has the units of length, and in this context, we'll assume meters (m). Let's proceed by analyzing the units of each variable in the formula:
- W is the molecular weight and should have units of kg/mol (assumed based on the context).
- V is the volume and has the units of m³ (cubic meters).
- R is the ideal gas constant with units J/(mol·K) = (kg·m²)/(s²·mol·K).
- T is the temperature and has units of K (kelvin).
With these units in mind, the formula L = 26 * W * V * R * T implies:
- Units of L = Units of 26 * (kg/mol) * m³ * (kg·m²)/(s²·mol·K) * K
- Which simplifies to = Units of 26 * m³ * (m²/s²)
Thus, to make the units on both sides of the equation equal, the units of the constant 26 must be 1/(m² * s²), making L have the units of meters (m).