To solve the given question, we need to identify which constant [tex]\( k \)[/tex] represents in the equation for entropy in statistical mechanics. The equation is:
[tex]\[ S = k \ln W \][/tex]
where:
- [tex]\( S \)[/tex] is the entropy.
- [tex]\( k \)[/tex] is a constant.
- [tex]\( \ln W \)[/tex] is the natural logarithm of the number of possible microstates (W).
Let's examine the given options:
A. kelvin:
- Kelvin (K) is a unit of temperature, not a constant. It measures the thermodynamic temperature and is not relevant to this equation.
B. Fludd's constant: [tex]\( 6.02 \times 10^{23} \)[/tex]:
- This is not a recognized scientific constant. The value resembles Avogadro's number ([tex]\( 6.022 \times 10^{23} \)[/tex]), which is used in chemistry to denote the number of molecules or atoms in one mole of a substance, but it is not relevant to the entropy equation.
C. Carnot's constant: [tex]\( 9.8 \times 10^{-8} \)[/tex]:
- There is no widely known Carnot's constant with this specific value in thermodynamics or statistical mechanics.
D. Boltzmann's constant: [tex]\( 1.38 \times 10^{-23} \)[/tex]:
- This is the correct value for Boltzmann's constant. Boltzmann's constant, [tex]\( k_B \)[/tex], relates the average kinetic energy of particles in a gas with the temperature of the gas and is essential in various statistical mechanics and thermodynamics equations.
Given this information, the constant [tex]\( k \)[/tex] in the entropy equation [tex]\( S = k \ln W \)[/tex] represents:
Boltzmann's constant. Therefore, the correct answer is:
D. Boltzmann's constant: [tex]\( 1.38 \times 10^{-23} \)[/tex]
