What is the meaning of W in the Boltzmann formula S = k In W? work times Avogadro’s number the number of microstates in a system number of molecules in the system work divided by Avogadro’s number the probability that a collision will result in a reaction
The Correct Answer and Explanation is :
In the Boltzmann formula ( S = k \ln W ), the W represents the number of microstates in a system, not work times Avogadro’s number or any other option provided.
Explanation:
The formula ( S = k \ln W ) describes the relationship between the entropy (S) of a system, the number of microstates (W), and the Boltzmann constant (k). This is a key concept in statistical mechanics and thermodynamics.
- S represents the entropy, a measure of disorder or randomness in a system.
- k is the Boltzmann constant, which is a physical constant that relates temperature to energy at the microscopic scale. Its value is approximately ( 1.38 \times 10^{-23} \, \text{J/K} ).
- W is the number of microstates. A microstate is a specific configuration of particles or molecules in the system, considering all possible positions and energies of the molecules in the system. The more microstates there are, the higher the entropy, which corresponds to more disorder.
In statistical mechanics, entropy is interpreted as a measure of uncertainty or the number of ways a system can be arranged at a microscopic level, while maintaining the same macroscopic properties (like temperature or pressure). If a system can exist in many different configurations or microstates, then the system has a higher entropy.
The logarithmic relationship in ( S = k \ln W ) indicates that the entropy increases with the number of microstates, but at a diminishing rate. This means that doubling the number of microstates doesn’t double the entropy; it increases it by a constant factor, due to the logarithmic nature of the function.
The Boltzmann formula links macroscopic thermodynamic quantities (like entropy) with microscopic behavior, bridging classical thermodynamics with statistical mechanics. Therefore, in this formula, W refers to the number of microstates, highlighting the connection between molecular behavior and the thermodynamic properties of a system.