Quantitative relationship between entropy and number of microstates The connecti

Question

Quantitative relationship between entropy and number of microstates The connection between the number of microstates, W, and the entropy, S, of a system is expressed by the Boltzmann equation where k is the Boltzmann constant per molecule (particle), 1.38 × 10-23 J/ K-particle). From this equation the entropy change, for a system can be related to the change in the number of microstates as Wfi Winitial where Wfinal in the final number of microstates and Winitial is the initial number of microstates. Part B 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 0.458 times that of the initial number of microstates? Express your answer numerically in joules per kelvin per particle. AS J/(K particle)

Explanation / Answer

B)

given

Wfinal / Winitial = 0.458

also

boltzmann constant = 1.38 x 10-23 J / K .particle

now

dS = k x ln ( Wfinal / Winitial )

using the given values

we get

dS = 1.38 x 10-23 x ln 0.458

dS = -1.0776 x 10-23 J / K.particle

we know that

for a reaction to be spontaneous

dG < 0

now

dG = dH - TdS

so

dH - TdS = 0

(-50 ) - ( T x -0.3 ) < 0

-50 + 0.3T < 0

0.3T - 50 < 0

0.3T < 50

T < 166.67 K

so

the temperature is 166.67 K

Related Questions

Navigate

• Browse (All)
• Browse Q
• Subjects

---