Question

A gaseous system undergoes a change in temperature and volume. What is the entropy change for a particle in this system if the final number of microstates is 0.418 times that of the initial number of microstates? Express your answer numerically in joules per kelvin per particle.

Answer 1

The entropy change is -1.2x10⁻²³J/K particle

Step-by-step explanation:

According Boltzmann equation:

`deltaS=klnW_(final) W_(initial)`

if x = Winitial

Then Wfinal = 0.418*x

and k = 1.38x10⁻²³J/K particle

Replacing:

`deltaS=1.38x10^(-23) ln((0.418x)/(x) )\\deltaS=1.38x10^(-23) ln({0.418} )\\deltaS=-1.2x10^(-23) J/Kparticle`